I agree with your overall point here, but would quibble that people might want public schools, et. al., to reflect some religion because of the influence on their own children - quite the contrary, people resent such influence unless such influence is substantially similar to their religious views.
And my ongoing point is that athiests, generally, have no motivation or incentive for such influence. Some people may infer that athiests’ desire to take the Christian doctrine out of schools and government as their attempt to push “the athiest agenda”, but that is just either myopic or simple-minded. It would be the consistent position of Muslim parents (or any other major religion besides Christianity), because at least they recognize how silly it would be to try and impose their views on everyone else’s children.
Perhaps TwistofFate suggests the same misconception here:
Is supporting the separation of church and state in law anti-religious? For example, would you agree that outlawing organized prayer in school is appropriate, but outlawing individual prayer (if you could) is anti-religious, and inappropriate?
It’s this confusion between not supporting any particular religious view and being anti-religion which is frustrating. I don’t believe most athiests are anti-religion. I think most athiests support religious freedom, and respect the many good qualities that religion brings to society (while at the same time detesting the many negatives as well).