Fair points on the Papel infallibility. I don't suppose Francis is going to issue anything of national strategic significance to America "from the chair" anytime soon.

With the SBC, I don't think they have a claim to exclusive truth to quite the same extent. My understanding is their claim is limited to speaking on behalf of the denomination, not for Christendom in totality. So a hypothetical Baptist president who took issue with a doctrinal position of the SBC could choose, for example, to leave the SBC and join some other baptist group, and still have a credible claim to be orthodox while also having confidence in his own individual salvation. The Roman church won't say it clearly these days, but my understanding is that orthodox Roman doctrine is essentially ex ecclesiam nulla salus, with the Roman church as the only "true church".

Also, at least the SBC is American. Someone being a faithful Roman Catholic is, in my mind, similar to someone who has a foreign nationality and a loyalty to a foreign government. Which is also an issue with the Biden administration, I believe, with Israeli-American dual nationals. That's a rabbit hole for another day.