I'm pretty sure the tag "vegetarian friendly" in the search engine i was using should be relabeled as "has vegetarian options." I have seen menus where it truly is vegetarian friendly. My favorite menus do things like list the optional proteins that can be added to salads, and other notes about substitutions and other changes. Those menus made me feel welcome.
I know many folks have diet-exhaustion, and if they have to adapt to one more dietary constraint they will ... whatever. But they don't begin to be as exhausted as the people who have to search the menu, look for warning signs, risk physical repercussions or existential* repercussions. The menus that indicate the restaurateur is truly welcoming of all patrons are a delight. Truly hospital and welcoming.
*Violating religious and other ethical dietary restrictions have significant repercussions that should not be sneered at.