Civil rights legislation, in the US at least, is designed to prevent the government from violating certain enumarted rights and/or liberties. There is no nexus between a private religion and the federal government, so the answer to your question that a civil rights action against the JWs would be thrown out before it ever goes to trial.
A little background info of general interest: http://www.constitution.org/grossack/bivens.htm
If a cop barges through your door without a warrant or probable cause and beats you to a bloody pulp, you have a civil rights violation on your hands. If your neighbor beats you up because you parked too close to his car, you don't have a civil rights violation, you have an assault and battery. The key is whether there was government involvment and whether a civil right specifically extended by legislation was violated.