Is it standard to compare two nouns?

Grammatically speaking, I would say that the comparison isn't between the two nouns, but the similarity of the subject's mannerism (The German Mr. Hafner's buttoned-up manner) to a boardroom as opposed to a barn.

So it's not so much comparing a boardroom to a barn, but it is like comparing a subject's similarity to one adjective (presumably used to describe their personality or characteristic) to another adjective.

Here the nouns are used as substitutes to adjectives because the nouns are meant to be representative of certain characteristics, so they are used as if they are adjective in a way here.

As @Michael_Lai suggests, it is not a plain comparison of two nouns, but a comparison of two attitudes (in this case, I guess to work).

Grammatically, I would say the construction looks ill-formed because of the metaphorical use of the terms "boardroom" and "barn". A correspondence between manner (tenor of the metaphor) and two vehicles (boardroom and barn) is traced to describe the nature of his mannerism. It looks more complex because of the comparison, but it could be divided into two:

Mr. Hafner is German and has a buttoned-up manner that is boardroom. Mr. Hafner is German and has a buttoned-up manner that is not barn.

The use of the two vehicles reinforces the meaning, emphasizing the contrast between the two working places. The properties of the boardroom are ascribed to the tenor (his manner), meaning that he's focused on benefits, efficient planning, marketing strategies... On the other hand, the barn represents a rural place where hands are used to work; it is more physical rather than intellectual. Also, a boardroom is usually seen as a clean organized space where you would wear a suit. In a barn, you have to get your hands dirty.

I think the question is not so much about "comparing two nouns" as about "matching two nouns". Specifically, I think it's about matching two count nouns without any articles.

Mr. Hafner is German and has a buttoned-up manner that is more boardroom than barn.

Here, both the matched nouns are count nouns, but you don't need any articles. In fact, it can even get awkward if you try to add articles:

?Mr. Hafner is German and has a buttoned-up manner that is more a boardroom than a barn.

Now, let's find out if matched count nouns work without any articles outside comparison. Here are a few examples:

The seven-figure coach is now an easy target for a takeover or a takedown. The Internet is both boardroom and back alley for angry fans and vindictive rivals to start whisper campaigns, demand firings and disclose N.C.A.A. violations. (New York Times)

In the past few years diversity has been a buzzword among brands and many are taking baby steps towards inclusivity, especially outwardly facing in advertising campaigns - but obviously this needs to be magnified across the industry from boardroom to design studio and every stage in between. (Glamour)

Chantal accepted Euro-smooches on either cheek of her self-composed face. Pete Smalley radiated that grab-the-bull-by-the-balls zest he no doubt displayed in either boardroom or barroom. (Fiction)

Finally, The Cambridge Grammar of the English Language talks about "matched nouns" (Pages 409-410):

vi arm in arm, back to back, day after day, mouthful by mouthful, side by side, mile upon mile [repeated nouns]

vii from father to son, from beginning to end, between husband and wife, mother and child [matched nouns]

...

The examples in [vi–vii] are illustrative of a number of expressions involving repetition of the same noun or contrasting nouns;

...

Similarly, in coordinate structures, bare NPs can optionally be used in repetition: We searched endlessly for a spring or a cave to spend the night, but neither spring nor cave could be found.

I know this response is late in the game, but I wanted to narrow the focus to the noun-comparison pattern that includes a linking verb: [to be] more NOUN than NOUN.

This pattern is indeed common in writing. It’s also linguistically “productive”—that is, it can be applied to produce practically countless instances of its kind with nouns of the writer’s choice (e.g. the street is more pothole than pavement, his book is more recipe than reflection, the river is more sandbar than waterway—see at end for more samples from the corpus).

With its imprecise measure and sometimes rhetorical whimsy, the construction doesn’t lend itself to use in, say, a science paper. But it’s widely accepted in formal writing, especially in journalism, where stylistic brevity and flair is valued.

It seems to me that these nouns following the linking verb usually function normally—as predicate nouns (e.g. like president in I am president)—and not like predicate adjectives (e.g. like presidential in I am presidential). But perhaps your particular example is a little different (we’ll get to that at the end).

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The [to be] more NOUN than NOUN comparison is used to weight two qualities or characteristics within someone or something, like this:

By now, the mud puddle is more mud than puddle, and the game of tag morphs into mud wrestling.
_{Source: The Washington Post}

We can imagine it expanded out using the preposition like (having the characteristics of) in front of the nouns:

By now, the mud puddle is more [like] mud than [like a] puddle . . .

Or we can conceptually understand it sort of like “more parts this and fewer parts that”:

By now, the mud puddle is [two parts] mud + [one part] puddle . . .

Nouns all, I would say. We can turn the nouns into adjectives by appending an adjective-forming suffix such as -like:

By now, the mud puddle is more mud-like than puddle-like . . .

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Depending on the nouns, the imaginary expansion might be better served by the preposition of, which combines with more to mean to a greater extent or degree:

There’s no simple list of actions departing CEOs should take; planning the outgoing transition is more art than science.
_{Source: Forbes}

. . . planning the outgoing transition is more [of an] art than [a] science.

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Quite often, these patterns employ rhetorical devices like metaphor, metonymy, and synecdoche. (Noun alliteration is also often involved.) In the first example below, horse and zebra are nouns used in their usual sense. In the second, those same nouns are used as metaphors for uncommon and ordinary:

[The zorse] was more horse than zebra but still had some features like some stripe patterns and a mane that stuck up, but it was tall like a horse.
_{Source: Reddit}

In contrast, many clinicians view the disorder as uncommon, more zebra than horse.
_{Source: Endocrine Practice (login required)}

Here are some more metaphors:

The Cubs’ interest is more smoke than fire, one person with knowledge of the situation said. They would prefer to land a younger, team-controlled starter.
_{Source: Detroit Free Press}

Smoke and fire are used to signal mild vs. blazing interest. (I would further call temperatures mild and blazing metaphors for moderate and extreme.)

And more:

Reminiscent of the song “Ocean Rain,” the placement of this track at the beginning is a hint that this album is more candlelight than glitterball.
_{Source: SortMusic}

There, we have both metonymy and metaphor. Candlelight and glitterball stand in metonymously for something like quiet evening vs. night at the dance club, which in turn metaphorically signal contemplative vs. kinetic ambience.

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In the metaphors above, the nouns stand in for adjectives (zebra = uncommon, fire = blazing, dance club = kinetic, etc.), but I don’t think that changes their function in the sentence; they’re still syntactically predicate nouns following linking verbs. Similarly: Even though we understand the metaphorical You’re toast to mean You’re finished, we don’t consider toast to function like an adjective there.

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Still, I can imagine a case for an adjective interpretation. Here’s another noun interpretation, as above:

The flavor is more cucumber than melon, with a peppy citrus kick.
_{Source: The National Gardening Association}

The flavor is more [like] cucumber than [like] melon . . .

Append an adjective-forming suffix: The flavor is more cucumbery than melony . . .

But if we imagine an elliptical noun flavor, we could argue that cucumber and melon are vestigial attributive nouns (which function as adjectives), stripped of their shared noun:

The flavor is more [like a] cucumber [flavor] than [like a] melon [flavor] . . .

Note that the adjective approach doesn’t work with our mud puddle:

? By now, the mud puddle is more [like a] mud [mud puddle] than [like a] puddle [mud puddle] (questionable)

So what’s going on with your sentence (inspired by the interesting New York Times article (The Business of Burps: Scientists Smell Profit in Cow Emissions)?

Mr. Hafner is German and has a buttoned-up manner that is more boardroom than barn.

Are these functioning as nouns?

? Mr. Hafner has a buttoned-up manner that is more [like a] boardroom than [like a] barn.

? Mr. Hafner is more [like a] boardroom than [like a] barn.

Hm, a manner or a person isn’t at all like a boardroom or a barn, like a room or building. Sure, there are things associated with boardrooms and barns, but there’s a missing link. What I see here is:

Mr. Hafner has a buttoned-up manner that is more boardroom [manner] than barn [manner].

Mr. Hafner has a buttoned-up manner that is more [like a] boardroom [manner] than [like a] barn [manner].

As with flavors above, if we imagine an elliptical manner, we can argue that boardroom and barn are vestigial attributive nouns functioning like adjectives.

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To summarize, the [to be] more NOUN than NOUN pattern is widely used, productive, and accepted in writing, formal and informal. I can understand arguments for adjective (quasi, attributive, or otherwise) interpretations in these patterns, but my sense is that these nouns mostly don’t jump the fence.

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Here are some searches from Corpus of Contemporary American English (COCA):

When the results appear, click ALL FORMS (SAMPLE): 500 at the top of the second column to see sample usage. From there, if desired, click a numbered row to see expanded context.

is more _nn1 than _nn1 (simple search—is with singular nouns; you’ll need to disregard false positives headed by the dummy there—such as There is more stupidity than hydrogen in the universe, and it has a longer shelf life. [—attrib. Frank Zappa])

_vb more _nn1 than _nn1 (all to be inflections with singular nouns; again, disregard dummy theres.)

_nn1 is more _nn1 than _nn1 (singular noun with is and singular nouns)

I would argue that this construction isn't comparing two nouns. I see it as creating an ad hoc path between the named items, where ordinarily, you wouldn't regard them as being connected.

... is more fiction than fact
... is part fiction, part fact

At the vary least, the more X than Y construction creates a need for some sort of middle from which to base the comparison. The second one does not.

This can work just fine within literal, figurative, metaphorical, or any other circumstances because it is a construction. And there really doesn't seem to be any restrictions on the sort of things that can be used as targets as long as the context lets you connect the dots.

We normally don't consider fact and fiction to be on a continuum, but we can force it with this construction -

... an autobiography that is (regarded by scholars as) more fiction than fact.

(I made this one up)

This construction does more than provide a simple apportionment of X and Y. The path connecting the two can be customized by context. We can place waypoints. In the above example, this is left to one's intuition. In a formal context, you would want to make sure there are waypoints on the path that help identify the middle.

The next challenge is to establish evidence-based protocols for goal-directed fluid therapy so that perioperative fluid management can become more science than art.

https://pubs.asahq.org/anesthesiology/article/130/5/677/18876/Perioperative-Fluid-ManagementTurning-Art-to