I hardly think sodomy is the primary feature of being gay. It is a lifestyle far more complex than sodomy.
Unclepercy, sodomy is the main, integral feature of male homosexuality (though I assume that under the law, a man and a woman could be charged for participating in sodomy). Incidentally, that reminds me, when I lived in Britain (1978 – 1986), sodomy (they call it buggery over there) was illegal, though of course, nobody was ever charged under the law (at least not in recent memory).
Traditionally, conservatives have had a much greater problem with male homosexuality than with female homosexuality (though lesbianism is a much greater threat to the traditional family that male homosexuality). I don’t know the reason for that. Perhaps women are considered virginal, pure, innocent etc., and in the old days it didn’t even occur to the lawmakers that women could participate in such ‘deviant’ practices.
So yes, homosexuality is more than sodomy. However, when they outlawed sodomy in old days, it was clear what the thinking was, it was to make homosexuality illegal.