Skipping OTAs is not what makes Aaron Rodgers unprofessional. It is not good, but he kind of earned it... like Brady did (not on the same level, let's be clear). Doing it on a new team is kinda dumb though. Especially when you pretend to be committed to winning, which Aaron Rodgers isn't. He is committed to Aaron Rodgers.
His attention-seeking and drama queen ways are what make him unprofessional - people were up in arms about Kaepernick kneeing for the national anthem and were saying to keep politics out of sports, which is fair, but Aaron Rodgers became a HUGE distraction when he decided to become a, dumb, social/political commentator.
Not to mention that the guy throws teammates and coaches under the bus all the time. No accountability. That is more bad leadership than a lack of professionalism though.
A consumate professional and a good teammate, he is not. A supremely talented QB? Yeah, that, he was.