What I worry about with IRV (which is usually how rank choice ballots are counted) is that if we assume that the proper compromise between people in a legitimate disagreement is usually no one's first choice, IRV specifically excludes that compromise.

In a hypothetical world, roughly evenly split on religion, where everyone would be pretty okay with secular tolerance, picking secular tolerance seems like the way to go. But if most people would somewhat prefer to try and force their particular religion on everyone if they can get away with it, secular tolerance will be everyone's second choice and will be discarded in the first round of voting... unless enough people recognize the dynamic and vote strategically rather than honestly, but that undermines the point of RCV.

I'll leave it to you to decide for yourself how much the real world resembles that hypothetical, but as I said it worries me.