Skill set. There’s no thematic reason that Jedi Master’s actual talents should be off limits to someone who is at the master level of knowledge, power, and experience, who is a fully trained Jedi. Leaving the order is irrelevant to that.
She
wasn't a fully trained Jedi. She left the order before becoming a Knight; she was still technically a Padawan of the order when she walked out on it, refusing the rank of Knight. Her own Master was not himself a Master (and never became one, because the Council - while letting him sit on it - refused him that rank).
Who is she learning this stuff from?
If you want levels in the Jedi Master PrC, you need to be a Jedi Master, which Ashoka Tano is not.
Like; if you asked her 'Are you a Jedi Master?' she would say 'No; I am not.
Compare also Anakin Skywalker. I wouldn't let Vader take levels in the Jedi Master PrC either, despite him being a lot more advanced in his Jedi training that Ashoka ever was, and even taking into account of him actually sitting on the Jedi council and otherwise qualifying for Mastery (and learning
from a Master in Obi Wan) by training a Padawan up to Knight rank (which she refused).
Vader is not a Jedi Master. He never was a Jedi Master either for that matter.
Lucky for him (and Ashoka) there are other PrCs that cover advanced Force sensitives from traditions other than the Jedi Order.
