FL does not turn down all felons. If your civil rights have not been restored, you are not eligible for admission to the FL Bar. I personally investigated convicted felons who were admitted to the Bar in FL. The Board considers several things including the nature of the offense, age during the commission of the crime, and what the person has been doing since the conviction. The Board considers the total person. Not all felonies are violent. If you are convicted of driving with a suspended license habitual in FL, that is a felony.
I would advise you to giving serious thought about your chances to be found morally fit to practice law. I can tell you that if you are thinking about Georgia, the Bar Examiners love to exclude those with a history of violence. I had a classmate that had a record and wasn't allowed to sit for the bar in Georgia.