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Notes -
I don't think I have much to add to the "you are being weird for making it an age thing" near-consensus emerging in the responses, so perhaps instead a question to throw back at you: do you have a script in mind for solving the same problem ("most of the group wants this person out but we can't find a good socially acceptable excuse to kick them") if it were not an autistic 18-year-old woman newcomer, but, say, an autistic 30-year-old guy? If you do have one, what is stopping you from applying that script here? If not, think of one, because that's a problem you will probably have to deal with earlier or later either way.
There's plenty of them in the group, and I have a general rule around including them as long as they take advice on when they are being anti-social spergs that people don't want to hang out with. The script to kick anyone out these days is pretty much: "You are making people uncomfortable about some concrete things, and we've talked about about it and you seem pretty unrepentant and unwilling to change so I think the majority of other people don't want to hang out with you." Unfortunately thats hard to apply here because the things that are making people uncomfortable, ie being an awkward 18 year old in a group of 32 year olds isn't something they can change.
Realising I missed a nuance on first readthrough, you seem to assume that the 30-year-old guy script has to involve concrete things that you can confront them over, which they could fix to get accepted into the group. The more interesting question there, though, is what you would do with a 30-year-old guy where there is no such thing. I've seen plenty of instances where some guy is just unlikeable, through no fault of their own; nobody can do anything about it, but having to be around him actively causes the other members negative utility, to the point that if they are not forced to stay they would sooner just leave the group. How would you deal with that situation?
I suppose I have a hard time believing someone is just unlikeable for no reason. It's almost always a personality quirk and the overriding question is how much is that quirk load-bearing on their identity such that if it caused problems, and they were asked if they could change it or at least hide it, would they? After some thought I don't think I've never met someone that was just unlikeable for no reason at all.
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Yeah, I think I have nothing much to say apart from +1ing @SubstantialFrivolity's comment. If you have a group consensus to make the policy essentially "no under-21s allowed", then it seems to be your job as the leader to own up to it and tell her. I should also say, though, that it seems possible to me that the consensus may not be as strong as you make it out to be, because you may have created social pressure to agree ("Are there any creeps in our midst who think it's not weird for us to hang out with this 18 year old child? No? Good").
Perhaps, if you need to justify it to yourself, you could think of it as a useful life lesson - a somewhat autistic girl I am friends with, though much older, does sometimes need to be persuaded (over her own stubborn objections) that 50 year old guys showering her with gifts and inviting her to go on vacation on them within hours of first meeting are not in fact just being unusually kind. Frame it as a lecture about social expectations in your circles and how all men are wolves; if you really want to drive it home, sacrifice some of your own and your group's good reputation and tell her that the boys can't control themselves around her and you don't like what it does to the group dynamic.
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