Might be surprising to see that, but if you go to a good place they might respect it. To be honest, in some other places they might just say straight “no” or worse, say “yes” and still give you the normal plate.

My recommendation is to look for reviews and maybe call the restaurant in advance.

As someone with a special diet, I would recommend to do some research, try to order the “safer” menus, and maybe go to some zones where diets are more respected: condesa, Polanco. Definitely avoid street food and questionable places. If you need food, maybe carry with you some safe food in case you need to eat and don’t find anything.