I think your suggestion of adding ways to exclude certain content is good and I would like to see something of the sort implemented. I'm not sure what would be the ideal solution, but for starters I think that adding the exclusion filter already in place as an option in the UI would be easy, quick and an uncontroversial first step. As it stands few people will ever learn about it. Plus using it is a chore since I have to dig out that thread to copy/paste the sequence to add to the URL. (FYI at the time of writing this comment it seems to be working fine for me.)
Most likely more tools are justified. Maybe blacklisting games with a certain tag from ever appearing to you (the filter, meanwhile, is just temporary and needs to be reapplied). Or just manually picking a game to never be displayed again. Maybe both or neither — it's not out of the question that there are better ways we haven't mentioned. Nonetheless I think the discussion would be worthwhile and productive.
Mind you I am developing a furry visual novel. You used exactly the kind of game I am making as an example of what you'd rather not see and I think you are perfectly valid in your request. Speaking only for my team and I, we know that our content is fundamentally niche and not up everyone's alley. We don't want to annoy people. As far as we are concerned adding options to filter out content would just improve the experience for everyone because your navigation would be just objectively better, it would be easier for everyone to find the games they want, and we the developers would relax knowing we aren't being a nuisance and bothering anyone. It's probably a safe bet that most, if not all users of Itch have a few things they'd like to filter out (particularly those who use it a lot.) I can't speak for other developers, but it wouldn't surprise me if many (particularly those making adult content) agreed with what I just described.