I guess I'm heterosexist.
I'd allow same-sex sleepovers, but not opposite-sex sleepovers once my kids hit puberty. I have no problem with premarital sex. I do have a problem with pre-independent-living pregnancy. If my sons are gay and are sexually active with boys who stay the night, I hope they're being safe. If they're not, they're the ones who have to deal with the consequences (i.e. STDs). It would be the same if I had girls who were sexually involved with girls (though the STD concern would be lessened). With opposite sex couplings, I have to worry about STDs, the power differential, and pregnancy. With the first, they're choosing to accept the consequences of their actions. With the second comes an increased chance of unwanted sexual contact, which creates a victim. With the third, you open a whole new can of worms, and there could end up being a baby who is dealing with the consequences of my decision to allow an opposite-sex sleepover.
Will kids have sex even when you don't provide them with an opportunity? Absolutely. They will find a way. I just don't want their mistakes to be on my conscience. I want to make the best decisions that I can for my children, and the best decision for my children is, I believe, to not allow opposite-sex sleepovers in the teenage years. I would likely welcome a girlfriend of my adult child into the home overnight during a visit, if my adult child was living independently (i.e. if they came for an extended visit over the holidays or something.)
There was a similar debate in a the winter 2010 Brain,Child magazine, btw.