Treating as non-canon is too easy a way out, a little thought can create a back story fleshing out a character.
For a Pure Blood (Sith) Jedi there are at least five options
1) Ancestors fled Empire and settled into Republic, enduring much prejudice
2) Orphaned during War, never knew Empire, Jedi found you
3) Family/Mentor killed in Sith infighting, be came Jedi to survive
4) Rejected Sith teachings, trying to redeem yourself, Empire considers you traitor
5) Double Agent, pretended to reject Sith teaching to learn Jedi techniques, doesn't fit into story though