No, pedantic people and Catholic apologists care. Everyone else figures, "Meh. Who gives a rip?"
I mean, seriously, if the only way you can feel good about yourself and your religion is to drum up some nonsense about Shakespeare being one of yours, then your religion can't be worth all that much.
The religious identity is the defining characteristic of a man. When the man happens to be a genius, his religious identity is a matter of importance to anyone who thinks that Shakespeare is important. I realize that to the modern halfwits it is all “meh”, but I am surprised that someone so uninterested still finds it necessary to insist on his philistine values.