Question: Three people were getting married to each other,  

   Though polygamous they were not.

All men they were in the marriage,  

   Though homosexuality was not in their minds.

They three share two parents,  

   Though they detested the notion of inbreeding. (And this was not, in fact, a consanguineous marriage)

Who are these men?

Hint 1:

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>  The first line makes you assume more than has been said. The "people" referred to "are" not what you assume "them" to be.
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Hint 2:

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>  45 chromosomes are identical (Not a single difference, even on the atomic level) between the "three men".
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Hint 3:

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>  Hint 2 does not say that the 46th was different. And two of the "three men" were the same person all along.
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Hint 4:

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>  Two of the men are the same person. This is a different hint from hint 3.
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Answer: 
Are they

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>  A man's past, present, and future
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Three people were getting married to each other

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>  They are getting married (as in joined/linked) all the time. The future self joins the present, and the present joins the past.
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All men they were in the marriage

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>  Check (baring any gender identity changes)
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They three share two parents

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>  Check, every person has the same parents as themselves
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Hilarious lateral-thinking answer: it's a marriage between

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>  **Three People Were** (a woman), who together with her siblings formed a gang called **They Three**.
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and

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>  **Each Other**, nicknamed **All Men They** (a man).
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*Three people were getting married to each other,*

Well, obviously!

*Though polygamous they were not.*

Polygamy has nothing to do with it!

*All men they were in the marriage,*

Indeed.

*Though homosexuality was not in their minds.*

No homosexuality here.

*They three share two parents,*

Siblings share two parents.

*Though they detested the notion of inbreeding.*

Nothing to do with inbreeding either!