A Brief History of Asexuality in Fandom
I'll add that fiction is a cyclic phenomenon. People create cliches and stereotypes based on motifs they spot a few times. Then other folks point that such-and-such isn't always true, or is problematic in some way, and the trope gains a variant as counterpoint to the original version. This continues for as many iterations as people feel like exploring that topic or character type or whatever. Like a fractal, it has infinite progression. And that's okay; that's how storytelling works. So ...
1. Behold: an asexual character!
Wow, wow, wow. Yep, there's an ace. How nice.
2. Bob the Ace doesn't like sex.
Okay, makes sense. I know Joe and Jane who are ace and they don't like sex.
3. Hey, not all asexuals hate sex. Anne the Ace likes sex, just prefers to do it alone.
Hmm, okay, good point. I know some other aces who like sex.
4. What does it mean if an ace character likes or doesn't like sex? How does that affect the story?
Well, it changes what kind of action is likely to happen, and how a given character will respond, and maybe what kind of interactions they'll have with someone else...
So then we get to have stories exploring all of those things, which is pretty cool. As a writer, a reader, and a literary scholar, I am in favor of stories and explorations. I'm not in favor of trying to cut off certain categories, although I reserve the right to ignore the hell out of stories I find displeasing and instead shower my attention and funds on other things I like better. It's good to have a lot of different people poking around at a pool of ideas so as to examine it from many different angles.
Once people start yelling about all the different things that are "really" what it's like ... then you just take a few steps back and look for the elephant. You should have most of his body parts in view.