No, it’s not that bad, basic psychics is something anyone can prove in their backyard, how do you ‘tamper’ with that… but it’s true that there are ‘unacceptable’ areas of research - paranormal anything, cryptozoology etc that can get your career ruined if you research something that’s too fringe. Or there’ll be no grants or PhD projects for it at all because the people that fund those want something they can make money off someday.
The flat-earthers are easily debunked, it’s a case of they see what they want to see and they ignore the data - they are all about the feelings and understand so little physics it’s not worth even trying to help them, they’re the opposite of rational scientific thinkers.