a person who is fluent in a foreign language can easily work as an interpreter

In order to be an interpreter one has to be fluent in the language , of course. Then he must be educated, intelligent, polite. They say, "Knowledge is power". So the interpreter must be competent in many branches of science, literature and arts.

Sure he can. Especially if that person has certain health or appearance issues, he still bloody well can
Who cares about articulation problems? Language skills are all that matter.
Even if psychological features or problems prevent someone from thinking straight, analyzing info, thinking fast, working under pressure, concentrating, he still can mumble something, even if he has a naturally disgusting voice that makes people want to puke!
Being morbidly fat is ok, too, even if that is drawing too much attention.
People must see who's doing the job - that's his moment, after all! There is no problem if the guy can't sit on his butt on hard surfaces due to spine problems or hemorrhoids or whatever, or is suffering from agoraphobia, you can just stand in that booth or refuse to go in. Not everyone likes it when an interpreter can't keep himself from swearing (cultural background, Tourette syndrome), but people can get used to it. Even a narrow range of interests is not a problem! You can always leave something you don't fully understand out or joke about it.