They might be motivated by political views, fact checking, etc, but the subreddits I've seen discussing it (baseball, Iowa) are focusing on the fact that you need an account to see anything now. Screenshots from X would still be permitted; just not direct links due to the degree of interaction with the site required to view the material.
It's sound reasoning, in my opinion. X either links you to an actual source or is a short post easily captured in a screenshot.
It's not totally insane reasoning but, like, people can just downvote links to Twitter if they want to, and/or use an extension to automatically redirect to a Nitter instance. The only people actually affected by censoring Twitter community-wide is those who would want to look at the context.
I think it's way worse to keep information from someone who wants to see it, than to let it be seen by someone who would prefer not to see it but isn't motivated enough to do something about it. Sort of by construction, actually - if the latter category really didn't want to see Twitter links, they would have done it themselves.