IIRC, the Pope is only considered infallible when they say they are. Otherwise they’re just speaking as the highest ranking member. So most of the time what they say is not treated by members of the clergy as the literal word of god.
Maybe other Catholics are more in the know, but this isn’t a distinction I was aware of when I was a practicing Catholic. That might be because the Pope really didn’t come up much at all. I’m sure he influenced policy, but his words seemed to come up in the news, and not really much outside that.
At least in my dialect (US northeast) clothes and close don’t quite share a pronunciation. They’re similar enough that you could probably fully elide the th sound, and I’m not sure anyone would notice.
When I pronounce clothes I can still feel my tongue move into the th position, and hear a small difference.