I've never heard someone say he made a decision about a job, etc, for "non-personal reasons". I don't suppose there's anything inherently wrong with the phrase, but I don't think it's necessary to coin it.
If you quit your job to get a better salary or because you were fed up with the incompetence around you or something of that sort, I think people would normally say that they quit "for professional reasons". If a politician resigned from office to run for another office, or if he quit his party because he had come to disagree with their policies, I think we'd say that was "for political reasons".
As those would be the "normal" reasons for making a career decision, it makes sense to use an affirmative rather than a negative term for them, i.e. say what it is, not what it isn't.
If someone says, "I quit my job for personal reasons", they normally mean reasons having nothing to do with the job itself, other than the time it takes. Like they quit to take care of a sick relative or because they wanted to move near family.
Of course when a politician says that he is resigning from office "to spend more time with my family", this is usually a code phrase for something like "because I was caught and I'm going to quit now as part of a deal in which I avoid going to prison". But that's another story.