In theory there is this dialog when entering the game page. At least when on a fresh browser session without cookies. But hover screenshots will still pop up, even if you hide the thumbnails. Also the thumbnails are what enable you to quickly sort games into categories. If you make devs hide the nature of their game, unintentional visits to game pages would increase. Also there are devs that have such content yet did not use itch for months or years. They would not update their thumbnails.
This might be naive, but since it is only certain tags, those tags must share a common attribute like being on a list and that list should be modifiyable, even if the mechanism can not trivially be disabled. So delete the tags from that list or remove that attribute, problem solved. That would be a solution that might not solve the underlying mechanic, but all of the symptoms.