Some religious social functions are denied to people who do not believe, or are unwilling to lie to their loved ones about their disbelief.

The exact same thing could be said about secular-humanist organisations - suggesting that there's nothing inherently wrong about such a standard even from your perspective. Sure, they outwardly profess being much more open and accepting than institutions of traditional organised religion, but the overwhelming majority probably wouldn't accept a creationist baptist or a wahhabi, for good reason - and the same goes for religious institutions. I don't think anyone should be forced to associate with people who openly reject and oppose their world-view, which seems to be what you're proposing.