The European Convention on Human Rights, Universal Declaration of Human Rights, and UN Rights of the Child give us a post-religious universalism that prevents the decent to nihilism postulated by Nietzsche.
The Human Rights charters that we value so much today are a recent product of Western, Christian thinking. Once their foundational Christian thinking has been rejected they become historical relics, of no more use in protecting future generations than the Maginot Line was in protecting the French in 1939. An atheist society would be built on quite different, utilitarian principles, where human life is no longer sacred. It would have its own charters.
Well, thankfully the above quoted rights surpass by quite a distance those rights 'allowed' to us by the Catholic (and some other) faiths.
It's quite frankly insulting poppycock to suggest that atheists would reject these hard-fought rights if the religious myths aren't upheld.