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: 
[lateral-thinking] 

This has been invalidated by an edit to the riddle stating explicitly that it is not a consanguineous marriage.

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>  Technically, they could be just three human males getting married. You're not polygamous until after you're married and, at this moment, they're only getting married. Homosexuality was not on their minds at this moment because they were all thinking about the three wedding cakes. The detested the notion of inbreeding (or marrying within the family) but that doesn't mean they wouldn't do it. Maybe they were being forced into the marriage by an evil alien overlord.
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Is it

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>  Male triplets in the womb, perhaps conjoined?
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>  They are married to each other in the sense of "any close or intimate association or union". It is an asexual relationship and they would share the same two parents. It appears to meet all the requirements. However, conjoined triplets are incredibly rare.
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