If that person just didn't want to have sex at all ever. But still wanted to be in a relationship, and they check all the boxes of what you look for in a mate, would you discard them for someone who's willing to put out, or would you just accept a sexless relationship with them ?

I personally don't think sex is important in a relationship and people can form meaningful relationships. That doesn't mean you shouldn't be with someone you find ugly or anything. You can still choose a partner that you find good-looking even if you're not looking to fuck them.
imo no one should feel pressured to have sex to be in a relationship, since everyone has the authority over their body's autonomy.