Personally I think toilets should just have their lids closed when not in use, regardless.

I agree. But the sole reason is that I don't want my cat to drink out of it (and potentially fall in). I'm also an enjoyer of the sit-down-wee, so no arguing there, either.

There are still good reasons for having other opinions about it, for people in other circumstances. And that's exactly why this is just a disagreement that can't be solved all and for once.