TLDR: Started off bad, got cleaned up, now mostly consists people fighting Russia. Not squeaky clean by any means, but not awful and mostly focussed on freeing Ukraine.
They started off far right with neo-nazi leanings and very nationalist. There was one particular individual was was specially awful iirc. He was removed at some point.
They had around 500 people until 2014 when Russia invaded. Then they were taken over by Ukraine, several key unpleasant people left and they were apparently 'depoliticised'.
The general view now seems to be that they started off far-right and now traces of that remain with some individuals. (Of course, Russia claims they're all signed-up members of the Nazi party but frankly there are more Nazis in Russia than Ukraine). To quote from wiki:
Many recruits joining the regiment are well aware of its past, and join up for various reasons, including Azov's positive reputation for training new recruits. While extremist elements remain, it is less driven by ideology than it was at its formation, and the chief motivation now is patriotism, and anger at Russian provocations and the attack on Ukraine.
also: The rest of the right-wing radicals who openly articulated their views were deliberately "cleansed" by the new regiment command in 2017" and that several Jewish members (including one Israeli citizen) are currently serving in the regiment.
However, rumours remain. Esssentially it seems that most (reputable) specialists in the far right movements think that they've cleaned up their act, but a few don't.