Wait, closing both is malicious compliance?
I generally believe if your anatomy requires the toilet seat in a certain position, it should be incumbent upon you to ensure it's in the right spot before you use it. 50% (ish) of people usually need it up, and 50% usually need it down, why should girls get to dictate this and complain if I don't preemptively put it down for them? Suck it up, buttercup. Put on (or I guess take off, in this case) your big girl panties and make it work.
That being said, I've just always closed the whole thing before I flush anyway, so now both of us are going to need to raise at least one layer of it before we can use it again. Closed lid reduces splashing the poop particles all over the place, looks nicer and cleaner, hides any racing stripes you haven't managed to pee off yet, etc. Just seems like the right way to go. Nothing malicious about it.
Edit: Jesus fuck, how many stupid gotcha replies are y'all gonna post here?! Yes, I am very clear on the fact that there isn't exactly a 50.000000:50.000000 split of males to females in the world. Yes, I am very clear that it is in fact possible, and sometimes preferred, for men to sit to pee, and that, having done it more than a few times myself, they also occasionally need to sit down to poop. Should I have said "want" instead of "need"? Eh, probably. None of that was anywhere near my point.
My point is that if you want or need the toilet seat in a particular position, that's on you, bucko. It's not my job to stage the toilet to your preference, regardless of what is or isn't going on in your undercarriage. I leave it 100% closed, seat and lid, every time, before I flush. Others may leave it in different positions. I don't know, I'm not them. Either way, if you want/need it a certain way, it's on you to put it that way, ideally before the pee starts coming out.