So I just ran across this puzzle, which has accumulated several close votes. I've seen other questions (kind of a flurry of questions) related to dobutsu-shogi "variant" of chess that had some downvotes (I didn't have 500 rep at the time, so I don't know about close votes).
Both of these questions involve the chess-variants tag, if my memory serves me correctly.
Neither of these questions (especially the first one) fall under what I would call a chess variant, and based on the votes, neither do some members of the community. However, there isn't really a hard definition on the site of what a chess variant is, so it's hard to get a good feel of when a question is off-topic or truly a chess variant.
So, should we have a harder definition of the "chess-variant" tag? There's already consensus on some variants, but not all.
If so, how should we define it? Personally, I would include any variant played on lichess.org as well as bughouse chess and maybe s-chess, but there may be more than that, and some lichess variants aren't super popular (horde, for example).
Also, we might want to make an exception for "find the illegal position" puzzles/questions.