Yes, you are correct in that the clause prohibits an 'official' religion. It's the common misinterpretation that it stops there.

I find it ironic that the original intent of the 'wall of separation' that was later described by Jefferson, described protecting the CHURCH from the STATE (I'm guessing to prevent a King Henry VIII-like 'reformation' or something like that). Nowadays it has to be used to protect the STATE from the CHURCH.