I can't speak for all Muslims but I don't mind at all if people give my children Christmas cards. This year for some reason they decided they wanted to do cards so I bought them a 10 pack each and let them write in them. I got ones that said peace because I think we could all do with a bit more peace in the world whatever our creed or lack there-of.
I might get them to do Eid cards next year and then when Christmas rolls around maybe they will have had their fill of card writing

TBH I think that any parent who is offended by their child getting a card from another child is being a bit precious but like I said I don't speak for all Muslims and I'm aware that many Muslims think I'm a tad too liberal in my thinking lol.