Would religion disappear or become a lunatic fringe, if not promoted by authorities anymore?

Imagine, no teaching of religion in school, no religious practices in mainstream media, no tax collection of governments for churches, no privileges for religious organizations.

Parents would not be allowed to keep their children stupid by restraining them from scientific teachings, such as sexual education, evolution and similar things. They may still teach them otherwise in private, but not keep them away from knowledge.

It should -not- be oppressive, like in the former communist countries, but still be tolerated as individual freedom, although referred to as nonsense, just like most people today refer to clairvoyance, astrology etc. as nonsense.

On the other hand, oppression by religious people, on topics like sexuality or disbelief, had to be effectively prevented.

Will such a policy make religion disappear or at least a belief of a small minority? Superstition, like belief in clairvoyance and astrology, were common in earlier centuries, but are now hiding in dark corners, with few people openly saying they take them serious.