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Ok hear me out: James T. Kirk.
I know that he's like THE famous womanizer and all, BUT does he have sex with these women? I remember an old blog post somewhere (not Tumblr) that kept track of every situation where it was possible/plausible for Kirk to have sex in whole TOS and it was VERY little. He flirts with everyone, sometimes out of genuine interest, sometimes to reach his goals, but it's flirting and kissing and so on. It's romantic. And with the women he is genuinely interested in he often ends up actually sad and heartbroken when in the end something happens to them or he has to leave. So I'd say it is pretty obvious that he feels romanticly attracted towards, well basically everyone in his vicinity, but we have actually no proof that he does feel sexual attraction. Soooo Jim Kirk is asexual.
Star Trek characters who are on the asexual and/or aromantic spectrums but who are not Vulcans, androids, or holograms. I'll start. Jean-Luc Picard :)