Growing up, my mom, a"h, insisted on changing tablecloths for meat and dairy meals. We had separate tablecloths, and we couldn't eat meat on the dairy cloth or dairy on the meat cloth.
Is this necessary? Assuming that the tablecloth is cleaned after each meal and there are no crumbs or other food items that could get on the plates (I doubt that even that may be a concern considering the crumbs are cold and probably batul beshishim in the worst case, but, even if not), could there be any concern or need for this? We are also not eating the tablecloth! (I tried that, once. It tastes like "Fab"!)
Even if this is not halacha, if your family has developed this as a minhag, do you need to follow it? Or, since this is a minhag based on a "false premise", one does not need to follow it?