This is funny. Everyone is acting like they havent done a crime in their life?
The guy you like wont be involved in your professional life. Nobody needs to know he is an ex convict. Everybody is being way too harsh here.
Findig a job will be a big difficulty for him (but not impossible as eventually someone will see past this guys past and hire him for who he really is as a person, his skills and experience) but if money isnt an issue then I dont see a big deal in my opinion. If you really can see a future with him and love him then whats the problem?
People make mistakes.
As long as you can really see that he is attempting to change is life and habits then you should be okay. Obviously, anybody would be skeptical even associating with an ex convict. However, get to know him more - maybe for a few months at least. See what his personality and habits are like now. Get to know his friends and find out what they do. You know? Don't just dive straight into a relationship with this guy.
All I'm saying is, his past shouldn't affect your future (if he has changed) and if this guy is really caring, sweet, and kind to you and makes you happy then it would be silly dumping him because he is a convict. I can understand your parents p.o.v though and good luck in whatever decision you make.