That the actual phrase "separation of church and state" does not appear in the Constitution is of no consequence (the phrase "fair trial" doesn't appear either). The principles of separation of church and state are undeniably and firmly imbedded in the Establishment Clause of the First Amendment.

Of course, this does not preclude people of faith from serving in government. Nor does it require them from abandoning beliefs or convictions that are formed by faith. That would be a violation of the Free Exercise Clause. It prevents, however, any govrnment action that promotes or favors one faith over another, or belief in God over non-belief.

For a government action violates the Establishment Clause one of the following must be present:

1. The Act must serve a secular, non-religious purpose;
2. The Act must not promote or inhibit religious practice;
3. The Act must not create an excessive entanglement with religion.

This test is from the USSC decision in Lemon v. _____ (the name escapes me).