MMT is both a description of the current system, a system that is already in place, and a set of policy proposals. So "believing" in MMT may simply mean understanding clearly the process already happening.
Your second would be the debate between Furman and Kelton on the Ezra Klein podcast, as I said.
I'll dig up a third cite. Like, one of the things in my head is the Kelton vs. Krugman argument, which I read on Krugman's blog, but that's not the best cite, since you're getting Kelton secondhand through Krugman there.
Happy to help. If you'd like to help too, you could cite a source that says MMT'ers feel like inflation doesn't matter.