Would it be acceptable for an atheist with atheist friends to insist that no religious symbols be worn?

Turn that on its head. Would any Christian you know, in deference to the atheists they knew were present, refrain from wearing their crucifix necklaces or fish symbols on their cars? Do any Christians you know insist on the removal of wayside pulpits or external crosses from churches in deference to the many atheists or people of non-Christian religions who would otherwise have to see them? No, thought not.

Alternatively, what if a believer, with many friends who believe, demands that everyone should say grace before they eat?

This is not hypothetical. It has happened to me on a number of occasions. It is an ignorant and insufferable thing to do. Unfortunately, unlike atheists, who have no beliefs but lots of doubts, many Christians and members of several other religions have this delusion that their beliefs are incontrovertible truths and that the rest of us should put up with them.