He meant the pledge of allegiance. First, it is a lie to suggest that the Democrats as a party took it out of the pledge.
But there is also the question of whether a person who doesn't believe in God, much less the God of conservative Christians, is capable of being a good American, respectful of the freedom of religion that is part of our country. To me the answer is a resounding yes. There is no impediment to an atheist, or Hindu, or Buddhist or Muslim, being as good an American as anyone else. Electing credibly accused creepy joe or someone that isn't part of a right-wing religious group doesn't threaten freedom of religion. It is simply a form of either paranoia or bigotry to assert something like that. But it does give a form of cover (as hypocritical as it might be) to support someone like very poorly chosen one, who in so many ways is the opposite of what Christians are taught to aspire to.