Interestingly, he said he has dated three therapists, which seemed like a weird kind of flex
This would make me think that he attracts the sort of women who see him as a project or have that weird complex where feeling that they're 'helping' someone boosts their ego. Not because I think therapists are necessarily all like that, but I think it's pretty odd to have dated three people from such a specific profession.
The fact that he said 'I'm not very good at relationships' is a classic thing of almost challenging you to win him over - it's quite manipulative, like a 'Can you be the special one who, unlike everyone else, can make me good at relationships because you're Not Like Other Girls' sort of thing. It's like he's offering himself as a prize for you to attempt to win.
The way he revealed the information (apart from saying 'Aspie' which is a term that always made me cringe myself inside out at its twee cutesiness even before 'Asperger's' became an outdated label) makes me very much think that he is someone who fully intends to use autism as his excuse for any poor behaviour and as a reason for always getting his own way.
I also think making a big deal about describing yourself as 'a bit odd' has strong 'Ooh, look at me, I'm so eccentric and wacky, aren't I adorable with my quirks, have you noticed my quirks, aren't they fun, I have made them into my entire personality' undertones to it.
Essentially, even if he is autistic, which he may not be, that isn't actually the problem - the problem is the way he perceives and presents it. I wouldn't turn someone down because they were autistic, but I would turn someone down who banged on about not being good at relationships / tried to make himself sound interesting by describing himself as 'a bit odd' / said twee shit like 'Aspie' / was a magnet for therapists with saviour complexes.
TL;DR - ditch him, he's a tit