Don't eliminate it. Tax it. I. e., eliminate its IRS 501(C)(3) status that makes donations to the church tax free. The RCC violates the rules for this status because they actively lobby both federal and state governments and even have large lobbying office in Washington. They also promote certain candidates and issues - 501(C)(3) charities are not allowed to try to influence elections. They should also not be exempt from property taxes. I would even go further and say the FDA should disallow them from promising immortal salvation in heaven (and damnation in hell), since that is obviously a significant health concern, unless they can prove efficacy to FDA standards.
Yes, this applies to many other religions, but lets start with the biggest offender. And yes, I realize I'm wasting my time to even write this post.