One reason is a misunderstanding of the First Amendment. We have been told over and over again that the separation of church and state requires that the government must not be involved with religious matters in any way. Another reason people think religion should be kept a private matter is a misunderstanding about religion itself. Americans believe that whatever they believe is true for them , but not necessarily for other people. But this cannot be so.
Religions provide an explanation of what is ultimately real .
Either there is one true God or there is not. Either there is salvation through Jesus, or there is enlightenment through meditation, or there is some other way to find fulfillment. Not all of these can be true in reality . This issue gets really tangled up when we bring in the matter of rights. The idea that everyone has the right to worship as he or she chooses has been transformed to mean that each person's choice of religion is true.