I see.
Why would you not expose children to nudity?
Cause I don't want to get arrested and put in the sex offender registry.

Don't you agree it's a matter of social comfort/discomfort due to a cultural payload we carry?
Yeah, sure, but regardless of the reason, parents have a right to shield their children from such things, and it's commonly accepted that nudity is something children should be shielded from.
And, where is the logical difference between a "liberty" and "the natural right to free exercise of religion"?
In particular: if there were a religion that shunned clothes (btw, I think there are a few very minor ones that do), wouldn't that mean that the prohibition of nudity is also an infringement or "the natural right to free exercise of religion"?
Yes, in that event it would be an infringement upon a right and not merely a liberty. However, the state still has a right to carve out an exception in the interest of the kiddies-- wont someone please think of the children? It has long been accepted, in my country at least, that the normal rules do not necessarily apply when it comes to children and that conduct by adults may be more strictly regulated when it comes to their interaction with children. Now sometimes I think this goes too far-- i.e. not requiring
mens rea when it comes to crimes like statutory rape and selling alcohol/tobacco to minors-- but I think saying people can't walk around naked in front of children is a completely reasonable limitation and, in practice, has a minimal impact on one's rights and liberties. Banning public use of niqab/burqua however, has no such justification and would have much more impact on free expression of religion.
All that being said, if someone in the US were arrested for being naked in an adults-only public place simply because their religion prevented them from wearing clothes, I would most certainly argue their First Amendment rights to free exercise of religion had been violated and the charges should be dropped.