Like a lot of things in this world, it's better in theory than in practice. It wouldn't be as big of a problem as it is, if abusers of the feature lost the ability to move questions when their behavior was discovered. That used to be the case...abusers would get demoted to a lower level and have to work back up to Level 7 to regain the question moving ability.
If there was a consequence for abusers of the moving ability (a permanent one), that would keep the feature limited to those who use it the way it was designed, to put misplaced questions in an appropriate category (not to move questions to arbitrary categories out of spite or to hide something the mover thinks is a violation). No, the feature wasn't created as censorship, since Level 7 users span across various political leanings or none at all.
Oath is considering changing who is allowed to move questions (it may not continue to be all users of a specific level) and/or having a consequence for abusing the feature. Unfortunately, it could be many months before any changes are made with regard to it. For now, those who ask questions should put them back where they belong if they get moved in an inappropriate category, and responsible Level 7 users should put questions they find out of place, into a suitable (or at least more suitable) category (which I do many times a day).