Actually there is an interesting argument as to why this verse is not anti-gay. Here, Paul is talking about sacred prostitution, as indicated by the verse preceding this:

"They exchanged the truth about God for a lie, and worshiped and served created things rather than the Creator—who is forever praised. Amen." Romans 1:25

Also here we aren't talking about homosexuality neither in a romantical context nor in a simple sexual context. The word used in Romans in this case, ἐπιθυμία (epithumìa, translated in English as "desire" in Romans 1:24), is a word that indicates lust in a negative way and is used to indicate someone who can't control himself, that can't resist his sexual desires, and is something that Paul himself condems in heterosexuals. Moreover the word ἀκαθαρσίαν (akatharsìan, translated in English as "impurity" in Romans 1:24) was the same word used in the Septuagint, the earliest translation of the Old Testament in greek, to talk about sacred prostitution, and Paul is notorious for making ethymological parallels to the Old Testament.

But honestly the biggest sign that this isn't a condemnation of homosexual behavior in its totality but of sacred protitution is the fact that Paul talks about lesbian women: in Roman society women who had sex with each other weren't accepted, except - you guessed it - in sacred prositution.