This is all personal preference. There is no issue to discuss here.

This assumes that men ever lift the seat. I’d prefer it be left up so that there is at least a chance I can sit on a dry, piss-free seat. Lowering a seat is preferable to the alternative.

I don't really understand what is the end goal here. It isn't minimising the amount of total work done, because for this optimal strategy would be just leaving the seat in whatever position it was used. Funnily enough, amount of times it needs to be put up is exactly the same it needs to be put down in absolute terms, but considering the "up" group is smaller than "down group", their perceived amount of times position should be changed is higher than the same for the opposite group. I. e. in group of one "up" and 9 "downs", "ups" need to change position of lid with 90% probability, and for every "down" it's only 10%. Huh. Of course overall it equalizes: 1×0.9=9×0.1.

Or is it some kind of "welcomeness"? Like, leaving the lid in the most probable expected position (which for equal gender usage would be "sitting" because people sometimes poop, usually not while standing; and because penis people sometimes pee while sitting (me often, but usually at home, not in public)).

Or is it something else?

If you have to sit and you have to go immediately you appreciate those that were considerate enough to engage in this simple act of decency.

Is peeing standing up something I'm just too intersex to understand? Like even before bottom surgery it was just more easy and convenient to sit down for it

Peak boomer humor. Congrats!

So, like, peeing into a toilet with the seat down, 100% keeps those tiny little splashes from hitting the tops my bare feet at home. So, when I pee in public toilets, I keep the seat down, to keep the urine off my shoes. I do wipe the seat if I miss, and I also spray if there is disinfectant. But I hear the smart girls squat atop the seat anyway.

Really, places where you don't have a urinal are sub optimal.

As someone with common sense and a little bit of decency: complaining about being asked to leave the toilet seat down when it benefits everybody is ridiculous

Unless you like sitting on the ceramic with no seat, I guess.