Livre d'Or

You're not wrong - but the 'public life' tends to be open only to a small number of religions - and the more support those religions have from the state, the less public life is open for a) atheists and b) other believers to follow *their* beliefs.

If schools have a moment of contemplation, nobody knows what you're saying inside your head: you might address a deity, you might simply go 'I hate this place'. If schools have a school prayer you're supposed to say aloud, then those who belong to that religion can practice openly; those who are not have to jump through extra hoops and may suffer consequences. And the less happy they are to sit through a daily prayer, the more problems they might invite.

'Not privileged' does not equal 'excluded'.