This is tricky, because I do not dare to speak for a god. What I write is my perspective on Him based on (shared) UPG and my interpretation of medieval material. I may be right, I may be wrong or I may be somewhere inbetween. I do not claim to speak the ultimate truth or to know the Gods’ true nature and will, so other Frey-devotees may have a different opinion on the matter. What you get here is mine and nothing else.
From my perspective, Ingui appears to be more concerned with love, joy and friðr than the gender of the couple. It’s about loving your partner and those under your care, protecting and looking after them, be true to your oath (whatever the words and terms), seek common prosperity and bringing joy to yourself and your partner – including sexual joy! And this can be done by both different and same-sex couples. Reproduction is not an issue: there are modern alternatives and there’s always adoption, which adds one or more children to the bonds of friðr.
Frey is, after all, one of the Vanir. He is said to have had sex with Freya, just as Njord is said to have fathered both of Them with His own sister. Incest, so say the medieval sources, is a Vanir custom. So is seiðr, the magic craft that entails accusations of effeminacy for the men who practice it. Frey even has His emasculating moment when He gives away His sword and I would expect a phallic god to be open about the use of the phallus: if women enjoy it, why not men? As long as you do it responsibly and respectfully, go for it! There’s a lot of fun and joy to have with a cock and men who want to can take part in it. There’s actually a common assumption among heathens that Frey tends to draw the largest number of gay worshipers, though I’ve never seen an actual statistic on it. In any case, the general picture of the Vanir is that of a sexually open group of gods, which is nothing new in the world of deities associated with fertility, pleasure and wealth.
If Frey is okay with formal marriage, does that apply to other forms of union? I would say yes. For those who do not want to marry and prefer a civil partnership or even a union with no legally recognized bond, the argument stands: Ingui cares more about love, joy and friðr than the gender of the couple or the way they choose to formalize their union. Make it sincere, make it binding and ask for His blessing. You’ll notice that I’m referring to choices: if a couple can’t marry because they’re of the same sex, then there’s no choice between marriage and civil partnerships. The option should be there, but that’s me talking and not Frey. Though I get the feeling He may agree.