How can a classless society exist with religion

Are classless societies and religion mutually exclusive? I believe that this is one of the major hurdles of communism; that the only way to remove socioreligious classes would be to ban religion, but that would cause much fight-back. So has anybody come up with a non-atheistic alternative to the problem of religion in communism?

ADDENDUM: I asked related questions on some religious Stack Exchanges:

• Christianity,
• Islam, and
• Hinduism