the two big ones are Romans 1:24 and Leviticus... 8? Peter absolved the faith of any obligation towards the old law (there was a famous bit in the bible about circumsision, this is also why a lot of reformed christians don't believe in things like tithes, prohibition, evangelicalism, etc.), and also the old testament was the civic and moral guidelines for an entire nation that sucked at following said regulations, so of course the law would go into exhaustive detail about how no, you can't cheat on your spouse that way. With full context, Romans 1:24 reads more as a condemnation of Pagans in Rome to establish clear lines between said Pagans and those former Jews and newly converted gentiles in the city. Paul also very famously wrote a dick ton of letters to different churches, so he might have been experienced enough by then to know that new converts would use whatever means possible to integrate themselves into local religions.
I need more secondary historical sources to back up that conclusion, which i'm working on. Outside of explicit proscription, a few handfuls of theologians see things like primieval man being man+woman and the marraige of the lamb to be an implicit proscription on gay marraige. But I highly doubt that. Some people point to Sodom and Gamorrah as an example of God hating homosexuality, and it's like... yeah bud, sure. the people of the city try to rape a literal angel, and homosexuality was just a bridge too far.
I've always personally believed gay marriage is holy in the eyes of God as long as it's ordained, & as long as sex before marriage doesn't taint the vow. Personally it's hard for me to practice what I preach, since i have a lot of cravings (sex, nicotine, men) that won't ever go away, but biblical study leads me to believe it's the striving towards God that redeems, rather than any sort of redemption that no man or woman could ever possibly learn.
(I use the word reformed christian here; fun fact, when someone describes themselves as that it means their faith is taken directly from scripture, out of a basic distrust of the 'telephone game,' as well as a personal charge from God to adhere to the word of God.)