[lateral-thinking]

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 on inbreeding but that doesn't mean they wouldn't do it. Maybe they were being forced into the marriage by an evil alien overlord. Besides, it'll be hard for 3 brothers to breed without the help of science.

[lateral-thinking]

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

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.