'What is important is ...' vs 'What is important are ...'

Important is an adjective. Be agrees with what, which here stands in for The thing which, so takes a singular verb.

I think the first one is correct

What's the most important is good customer relations.

The second one seems a little unusual as the verb subject is "What's most important".

There's no doubt that the subject of these sentences is what's most important, not good customer relations. If the speaker had intended to express the subject as plural, they should have said what are most important instead, in which case the subject should have been followed by are good customer relations:

What are most important are good customer relations.

But the speaker didn't express the subject as overtly plural. So there's no need to make the matrix verb plural just because the predicative complement good customer relations is plural.

Now, some speakers might think that the subject is good customer relations and use the plural verb are as in the second sentence.

What's most important are good customer relations.

But I'd think these speakers are confusing it with a legitimate inversion where the subject is indeed plural good customer relations:

Most important are good customer relations.

*Most important is good customer relations.

Both are acceptable, as @BillJ said in his comments. And to prove him right, I will just quote American Heritage Dictionary that addresses this problem in a long usage note for "what"(especially point 3):

Clauses with what as either subject or object may themselves be the subject of a sentence, and sometimes it is difficult to decide whether the verb of the main clause should be singular or plural.

1. When the what in the what-clause is the object of the verb and the complement of the main clause is singular, the main verb is always singular: *What they wanted was a home of their own.
2. When the complement of the main sentence is plural, the verb is most often plural:

• What American education needs are smaller classes,

though one also encounters sentences such as

• What the candidate gave the audience was the same old empty promises.

3. When the verb in the what-clause is singular and the complement in the main clause is plural, one finds both singular and plural verbs being used. Sentences similar to both of the following are found in respected writers:

• What drives me crazy is her frequent tantrums.
• What bothers him are the discrepancies in their accounts.

When the complement of the main clause consists of two or more nouns, the verb of the main clause is generally singular if the nouns are singular and plural if they are plural:

• What pleases the voters is his honesty and his willingness to take on difficult issues.
• On entering the harbor what first meet the eye are luxurious yachts and colorful villas.

You will never go wrong if you use your verb in the singular in "what is important is". However, we cannot dismiss as incorrect the use of the verb in the plural (i.e. "what is important are" + plural predicate) because of its plural predicative which follows after. We must simply be aware that it is quite uncommon, as you can see in this NGram:

Here is an answer on the BBCLearningEnglish site that explains it:

We use the singular form of the verb when the subject is a clause

• In good dental care, what is important is regular brushing and a good mouthwash.

• What we are interested in is wheat varieties.

However, if the idea of plurality is strongly present as it is in the sentence about wheat varieties, then this rule is not always followed. So it is quite conceivable that you might also say:

• What we are interested in are wheat varieties.

Of course, if you turn the sentence round then you have a plural subject which forces the plural form of the verb:

Wheat varieties are what we are interested in.

The verb to be, when it acts as a copulative, has no lexical value. In broad terms it is the same as the mathematical "=".

Traditionally, the first NP is assumed to be the subject, and the second the complement: The verb agrees with its subject.

"What is most important is good customer relations.*

or

*Good customer relations are what is most important.

NB "what" = the thing that