By the way, if atheist privilege to eliminate religiously informed ethics from the public sphere had prevailed, the movement for conscientous objection would probably have been too weak to be successful.

That's turning social reality on its head. It's evidence of religious privilege that conscientious objectors who claimed to be based on secular humanist principles would have been treated more harshly than those claiming religious principles. Possibly because the authoritarians administering military service were inclined to accord religious objections greater respect. That is religious privilege. Not a "failure of atheist privilege to prevail".

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman