Private lawsuits can seek relief that otherwise would be beyond the state's power under the 1st Amendment. For example, speech itself can be penalized by a court if it violates a non-disclosure agreement.
Cool, I'm sick and tired of Christians forcing their beliefs on me. I'm sure that if a law were passed allowing me to take private action and sue people for being Christian that would be fine since it's not the government taking action on religion?
Not really. It's an artifact of contract law.
Could you give an example that is not a byproduct of a contractual provision?