Those civil rights are protected only when the GOVERNMENT tries to impede them. Private citizens, religions, individuals, etc. can infringe away. The courts will step in only when the government is acting (or a case can be made that private action was for the government-like company towns keeping the JWs from going door -to-door.). There is quite a bit of expansion into the private sector here, but mainly through education (private schools) and through private employers (but the courts make it government action through the Interstate Commerce Clause).
The WBTS can infringe away, since it is not acting as an agent for the government. The only thing the constitution prohibits an individual from doing is owning a slave. Everything else in the constitution is prohibitions on what the GOVERNMENT can do.
Hope this clears up why people can't sue WBTS for infringing on free exercise of religion.
Shoshana