In the sexuality domain, are "heterosexual" and "straight" exact synonyms?

No, in English, "heterosexual" and "straight" are synonymous, with each of "homosexual," "bisexual," and "asexual" being in a separate "quadrant of sexuality." One cannot fall into more than one of these categories.

Straight is a metaphor, and means heterosexual only in a limited set of contexts.
Most of the time it doesn't mean that.

• It's 20 miles straight North to the border.
• I'm pretty sure she's been straight with me about that.
• Stand up straight and look straight ahead.
• Honestly, you're such a straight arrow; would it kill you to ignore that stuff?
• Be sure to position it straight up; we don't want to have to brace it.

The metaphor theme is Morality is a Straight Line, which is part of Life is a Journey.
The unspoken, but very prominent, presupposition of this metaphor theme is that homosexuality
is immoral, while heterosexuality is moral, and therefore straight.

Folks who at various times in their lives display gynesexual characteristics and at other times display androsexual characteristics are amphisexuals — or simply human, if you prefer a shorter word. Human sexuality is a fluid continuum, not a Boolean characteristic.

Particularly when used as noun rather than as adjectively, words like homosexual and heterosexual carry heavy connotations of morality, exclusivity, culture, identity, and expression. They work better to describe relationships or acts than they do to describe people. Used to describe people, these terms can easily come off sounding judgemental, and are seldom 100% accurate in all regards anyway.

Someone who is sexually attracted to one gender may or may not be sexually attracted to the other gender, and they may or may not be sexually repulsed by the other gender. They may form romantic attachments with only one gender yet engage in sexual behavior with both. Finally, all this is much more fluid than the clinical-sounding terms may suggest, as even within the same individual it can vary significantly with time and circumstance.

For example, I have personally known both men and women who identify as “straight”, yet who sometimes engage in non-romantic sexual activity with members of their same sex. Clearly, they are not repulsed by their own sex, yet at the same time they do not consider themselves “bisexual”. Indeed, they reject that term if applied to them, probably because of the social connotations, and perhaps because they do not form romantic relationships with their own sex.

This actually works the other direction, too. I’ve also known both men and women who, despite self-identifying as “gay”, have been known to have sexual (but not romantic) relations with members of the opposite sex. These folks might be somewhat less likely to reject the “bisexual” label with quite the same vehemence as the corresponding self-identifying “straight” people often are. But they still think it a mere technicality, and so do not change their constructed cultural identification just because of some occasional dalliance outside of that consensus construct.

I’m reminded of this bit of dialogue from the musical Hair:

Prison Psychiatrist: And men?
Woof: What do you mean...?
Prison Psychiatrist: You have any sexual attraction towards men?
Woof: You mean if I'm a homosexual or something like that?
Prison Psychiatrist: Yeah.
Woof: Well, I wouldn't kick Mick Jagger out of my bed, but uh, I'm not a homosexual, no.

Probably that could stand some updating for today’s audiences, swapping in someone younger for Mick Jagger, but the expressed sentiment is ageless.

Straight in terms of sexuality is more likely the opposite of 'kinky'. So, you could have a 'straight' homosexual, or a 'kinky' homosexual. Or more to the point, a 'straight' heterosexual, or a 'kinky, not straight' heterosexual.

In common usage (which at the end of the day is what matters - we communicate to get a point across), heterosexual and straight are synonymous. That is, if a person is described as either, they are assumed to be exclusively attracted to the opposite gender; if a relationship is described as such ("He's in a heterosexual relationship right now"), generally it only implies that this particular relationship is one between a male and a female.

In terms of expressing attraction to one gender without further implications: "gynephilic" and "androphilic" and/or "gynesexual" and "androsexual" are words that are often used, or simply "men who have sex with men" (edit: note that this refers to action and not attraction, which appears to be your intention) as has been mentioned, since it makes no mention of sexual orientation. However, in conversation it's probably easier to just say "he likes girls".

I have some doubts about straight and heterosexual being exactly synonymous, though they do overlap a lot.

Heterosexual/homosexual are not polar. People are not 100% one or the other. There are degrees in between, usually graded as homosocial(likes the company of their own sex) > homoerotic(gets excited by their own sex) > homosexual(has sexual relations with their own sex).

If we accept this homosexual continuum, then straight and heterosexual do not have to be identical. A "bromance" for example, (my apologies for using such a ridiculous word...) is probably straight as in 'normal' and not sexual, but not strictly speaking heterosexual as it is taking homosocial to extremes. Another example is the WW I poetry of Siegfried Sassoon, which is undoubtedly straight but still verging on homoerotic.

In the same light, it is worth bearing in mind that while male/female are polar and genetic, male and female are social constructs and therefore not polar. Think drag queens, lady-boys, ladettes, etc.

Straight is simply a slang term for somebody who is predominantly heterosexual. In ten years from now, the term "straight" may no longer exist as slang for the same just as it probably didn't in the middle ages :).

In the sixties there could be some confusion between straight as in "straight arrow" & not hip and gay & straight.

I believe it was when gay was first being used as a polite version of queer that straight seemed to pop up as its opposite. Queer had more restricted in use, it was a sort of a form of tagging. I don't think queer & straight were used as opposites.

"Straight acting" is a term that has a controversial history of its own - like "passing."

And I agree with the comments above about there being such a extended continuum of sexuality that there is no pure sexual response - it's all tinged with various admixtures.

As others have noted, heterosexual and straight both refer to the portion of the heterosexual–homosexual continuum where one is predominately attracted to the opposite sex. The two words vary somewhat in connotation and register, so they are not exact synonyms, but neither one suggests significant homosexual activity, nor do they rule out past or incidental homosexual activity.

If you would like a term that specifically suggests more openness to homosexuality, consider heteroflexible or bi-curious:

Heteroflexibility is a form of a sexual orientation or situational sexual behavior characterized by minimal homosexual activity despite a primarily heterosexual sexual orientation that is considered to distinguish it from bisexuality. It has been characterized as “mostly straight.” Although sometimes equated with bi-curiosity to describe a broad continuum of sexual orientation between heterosexuality and bisexuality, other authors distinguish heteroflexibility as lacking the “wish to experiment with . . . sexuality” implied by the bi-curious label. The corresponding situation in which homosexual activity predominates has also been described, termed homoflexibility.

Straight but not narrow is a similar idiom used to describe people who are heterosexual but open-minded about homosexuality.

"Straight" and "Heterosexual" are clearly not etymological synonyms, even in the context of sexuality as they arose quite separately and are only loosely tied in certain contexts (but never equivalent, in my opinion).

"Straight" is many times employed in a moral sense for much more than sexuality; "Nah, man, I'm straight" can be a refutation of drugs as well. This use was made popular by the Straight Edge subculture of hardcore punk that abstains from alcohol, drugs, and promiscuous sexual behavior. Their use of the word 'Straight' was appropriated from previous usages of the word.

This usage hearkens back to 'strait and narrow', in print in 1706 and 1712 (likely in use before then), and means "A conventional and law-abiding course."

in A Vindication of the Government in Scotland: During the Reign of King Charles II, 1712: "Strait and narrow is the way that leadeth unto life."

- Strait and Narrow Etymology

From this context, especially those who typically employ it, the 'conventional' / 'straight' lifestyle does mean fully heterosexual; not mostly heterosexual, not bi-curious, etc. It also does not include drug use, or promiscuous sex (even of the heterosexual variety).

Heterosexual, by contrast, lacks the moral judgments or 'lifestyle' assumptions that go along with "straight" - as examples, you could be a heterosexual prostitute (not "straight" sexually - promiscuity and premarital sex were not on the 'strait and narrow' path), or a heterosexual drug user (not "straight" in lifestyle), or completely asexual by choice (for example, a chaste priest would also be considered "straight" by lifestyle).

The term "heterosexual" was first published in 1892 in C.G. Chaddock's translation of Krafft-Ebing's "Psychopathia Sexualis". The noun came into use from the early 1920s, but did not enter common use until the 1960s. The colloquial shortening "hetero" is attested from 1933.

- https://en.wikipedia.org/wiki/Heterosexuality#Etymology

Further, you could easily be 'mostly heterosexual', 'somewhat heterosexual', 'occasionally heterosexual', and other qualifiers that expose the fluid concept of sexuality, which is in sharp contrast to the binary nature of 'straight' vs. 'not straight' as a moral concept.

There is a term for a lesbian who has never had sex with men: "gold star." This is sometimes generalized to any homosexual who has never had heterosexual intercourse. The term would be meaningless if gay/lesbian was exactly synonymous with [an exclusively] homosexual [person].

Kinsey demonstrated that latent sexualities frequently exist and that some people have mixed desires. Whether straight is synonymous with [an exclusively] heterosexual [person], really depends on your world-view/identity politics.

Barbara Kipfer & Robert Chapman, Dictionary of American Slang, fourth edition (2007) does a nice job (if you can get past the "sexually deviant" wording) of suggesting the array of meanings straight can have as a slang term:

straight adj 1 Unmixed; undiluted; NEAT [example omitted] (1874+) 2 Not using narcotics; not addicted; CLEAN (1950s+ Narcotics) 3 Having had a narcotics dose, esp the first one of the day [example omitted] (1946+ Narcotics) 4 Heterosexual; not sexually deviant (1941+ fr homosexuals) 5 True; honest and direct [example omitted] (1530+) n A tobacco cigarette; SQUARE (1960s+ Musicians & students)

So when Jonathan Richman sings, in his 1976 song "I'm Straight,"

So this phone call today concerns Hippie Johnny./He's always stoned; he's never straight./I saw you today, you know, walk by with Hippie Johnny./Look, I had to call up and say, I want to take his place./See, he's stoned—Hippie Johnny./Now get this: I'm straight, and I want to take his place.../Now I've watched you walk around here. I've watched you meet/Your boyfriends (I know) and you tell me how they're deep./Look but, I think, if these guys, if they're really so great,/Tell me why can't they at least take this place and take it straight?/Why always stoned, like Hippie Johnny?/I'm straight, and I want to take his place./I'm certainly not stoned, like Hippie Johnny is./I'm straight, and I want to take his place...

he's using it, in the finest poetical tradition, to imply perhaps every sense of straight in the Kipfer & Chapman entry except "having had a narcotics dose" and "a tobacco cigarette." He's certainly not limiting himself exclusively—or even primarily—to the narrow meaning "heterosexual."