I talked to them over discord, they're aware of this issue, it seems this is a non-trivial problem, the way search-by-tags work is not the same as just a regular search (in which is age protected). Hopefully this gets fixed soon.
Viewing post in Delete all ADULT games
Tag "search" works just fine with the nsfw protection. It is just as age protected as it advertised - with the exception of certain tags.
Try it with this one (setting on and off)
https://itch.io/games/tag-science-fiction/tag-story-rich
And then try that one (setting on and off)
https://itch.io/games/tag-adult/tag-science-fiction/tag-story-rich
It is obviously an arbitrary list of tags and to my understanding they would just have to clear that arbitrary list to deal with this issue. Or did they hardcode that list somehow? It "works" for adult, erotic, eroge and some others, even non featured tags. Curously, it does not work for sex.
Also, I told them about the issue in April, almost a year ago. Request 152691.
And as a reminder for anyone wanting to try all this, if you have adult content released yourself, you cannot deactivate the adult setting for your account. Just browse for it without being logged in.
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.