You make the assumption that this is mysoginy. It’s not. Not at all.

Women who desire to stimulate the interest of men behave in the way they think will allow them to do so. If they want to attract the attention of certain types of men, they tailor their behaviour in a way that corresponds to that kind of man. In the example you gave, the character wants to appeal to the type of man that isn’t interested primarily in a woman’s looks, so she signals that obsessive grooming is not her top priority.

Here’s why it’s not mysoginy. Men do the same (also LGBTQ).

I happen to like an intellectual challenge, so I respond to women who provide that. Does that mean I’m using my patriarchal privilege to manipulate women into behaving that way? No!

You’re seeing mysoginy and sexism in everything, but there’s no good reason to be so paranoid. I’m not saying it’s not a problem, but it’s not the primary factor in all social behaviour. Sometimes there isn’t a hidden subtext.