If you actually look at the history of body hair removal, it's almost always been associated with cleanliness and purity and from there social status.

The modern variation started with darwinism and the assertion that body hair was more primitive and undeveloped. Hairlessness was then cast as more evolved. Spectrum of ape to human has a clear hair gradient, so obviously less hair means less ape-ish, and hence more desirable.
In the past few hundred years the evolution aspect has been giving way to the purity and cleanliness aspect again.

The sexism is in who our society finds purity and cleanliness more important for. Trying to tie that double standard back to pedophillia just makes people more prone to dismiss the entire thing.

The driving factor can be seen more in how people talk about beards, but also womens. People say clean shaven men look clean, professional, and so on. We all know what images come to mind if I say to picture a neckbeards room.
People aren't infantalizing men by appreciating a removal of a prominent secondary sexual characteristic.
For women, you said it yourself:

finds natural body hair on women to be grotesque

You didn't say "old", or any of the myriad fucked up terms some people have for women older than 25, you said "grotesque". Society finds it gross or unclean.

The sexism is right on the label. You don't have to go digging for it.
Society has significantly higher standards for hair removal for women than men, likely related to how society has higher standards of "purity" for women than men. Men have an "out" where the masculinity of male hair can also be positive, but there's no corresponding feminine hair boost.