Well, a couple things here.
First is that you're overlooking the first definition from Thayer's: the bed guard, as I mentioned. And WHY were these men trusted with the women...? Those people are not, by necessity, celibates. There is nothing in the definition saying they were. They are simply men who, for whatever reason, are trusted not to make sexual advances on women.
Second, while it is true there is no indication of permissiveness towards including homosexuals in marriage, the passage does at least beg the question of whether there was some degree of acceptance by Jesus of "natural eunuchs" -- who may have been homosexuals or asexuals. Keep in mind, Jesus was a radical for his time.
I am not the only one who thinks so. Here's a theological journal that also thinks homosexuals may have been included.
http://www.ajol.info/index.php/actat/article/viewFile/52578/41183
Dr. Robert Gagnon, who actually is none-the-less anti-gay, accepts this definition as well.
"Probably “born eunuchs” in the ancient world did include people homosexually inclined, which incidentally puts to the lie the oft-repeated claim that the ancient world could not even conceive of persons that were congenitally influenced toward exclusive same-sex attractions…"
One does not come "from birth" as a religious celibate, and the natural eunuch is explicitly included.
Does this endorse expressing one's homosexuality? Well, given that there is nothing in the overarching definition of "eunuch" which indicates they are therefore celibate, it might. Jesus includes all the possible types of eunuchs, even those who may not be celibate. Jesus does talk about individual paths a fair amount, and shows a much more nuanced concept of humanity than most other writers. So this is possible.
If no bonding as one is ever possible in the first place for you as a gay person, do you still burn for not achieving the unattainable? Perhaps not. I mean, let's keep something in mind: God allowed concubines too, and people in that arrangement didn't burn because they're not married. You could be a man of God with a concubine (or 10). There is an argument that scripture allows this for exactly the same reason you gave for slavery: it was simply part of social structure at the time. If you get a pass on concubines, why is it not possible the "natural eunuch" might get one as well, according to a radical Jesus who clearly recognized the natural origins of attraction?
Evidently, not all sex outside marriage is sin. None of it is necessarily encouraged, but it is at least tolerated in some cases.
Yes, much of this is left a bit murky. Jesus evidently didn't care very much. He went to the trouble to talk about these things, but never issued any condemnation, unlike his rather sex-obsessed follower, Paul.
We do know that Jesus was likely much more accepting of it than society as a whole, Hellenistic Paul especially, and that this would be par for the course for his stances, really.
We do know some types of eunuchs were not labeled such because they were celibate, or impotent.
We do know not all sex outside marriage led to damnation.