Lawyers should never get disbarred, and drivers should never lose their licenses, for doing anything that the Constitution gives them the right to do.
Has it not occurred to you that professionals could lose their licenses for reasons that at are not solely political? Like professional malpractice, or advocating for quackery? (There’s a line to be drawn there, too, about what constitutes reasonable standards, but you seem to be suggesting that there be no standards at all.)
For malpractice such as leaving a scalpel inside of someone or amputating the wrong appendage, sure. But there's no Constitutional right to do either of those things. As for "advocating for quackery", the government forbidding someone for practicing medicine over that absolutely flies in the face of the First Amendment.
Which might be a tricky distinction sometimes, especially in psychology, because (1) some beliefs and speech aren’t exactly object-level, but aren’t quite political either; (2) previously non-political, purely object-level issues (eg. treatment approaches for trans people) sometimes become seen as politicized (make no mistake, JP very much played a part in making it so), or conversely lose its previous political connotation.
This doesn't seem obvious to me at all.
Many (most?) professions have things you need to do that are outside of considerations of any country's constitution.