I am going to leave aside any controversial topic, to focus on a detail that No Time To Play did not mention.
The tags are not placed by Itch, but rather each developer places the tags that they consider appropriate for their game.
The tags work cumulatively. In other words, if someone has a game about "birds" and "apples" and places those tags, if tomorrow you search for games with "birds" that game has the tag "birds" and it will appear in the search, even if it also has the tag " apples." This is how all search engines work.
Your threat is not against Itch, but against all the people who have made those games.