We aren't too strict - not that DS is old enough to worry yet.
But we are vegetarian so of course are very strict about that and we often get people offering meat to DS - in front of us!! So I hate to think what will happen if he is babysat by them. My mum wouldn't give it to him but not sure about DH's side. I think if you are clear about the reasons why then they should have to accept that. Whether they actually do or not is unfortunately different. I think let them know that your kids have certain allergies to preservatives and if they still resist then maybe you could find some easy reading literature. It is after all, quite a common problem these days.
HTh