[hutzlibu]

Well, I am not a american, but as far as I understand it, it does say it.

"The First Amendment (Amendment I) to the United States Constitution prevents the government from making laws that: regulate an establishment of religion; prohibit the free exercise of religion;"

Any incorporation of religious organisations into the state fabric, would be an "establishment of religion". So of course open religious people can be part of the government. But the government may have no favourite religion it subsidizes, teaches in schools etc. or prefers in any way.