There is some truth in this, in the sense that anti-abortion is overwhelmingly formed by religious sentiment.I don't understand why we are still talking about religious stuff. If your religion tells you not to have an abortion, have at it (or not, as the case maybe be.) Religions placing that expectation on everyone else is the opposite of what America stands for. (Well, at least pretends.)
However, religious people also have a right to see their beliefs enacted in policy. If a religion states that everyone should look after the poor and it informed the attitudes of the religious, we could hardly refuse their democratic mandate to pas generous welfare allowances because it was rooted in religion.
So the question here is perhaps the framing of the argument. Intelligent Design in schools, for instance, has been routinely bounced because it has no justifiable scientific basis whatsoever: the smoke and mirrors don't hide the fundamentally religious nature. Abortion however is trickier. The argument "Ban it because my religion says so" would breach secularism. But they don't frame it like that, they frame it as "life begins at conception", which is undoubtedly defensible at some level. Sure, we all know they're making that argument because of religion, but whilst they have an independent secular argument that stands on its own two feet, it is up for serious consideration.