Most people do have some idea why they are their family's black sheep. If the core reason for your marginalization is some moral or ethical transgression that you need to make amends for; such as my brother-in-law's theft of several thousand dollars from his dying father, then decide if and when to begin the long journey of repairing trust. You might start with a mea culpa (a heartfelt admission of wrongdoing) coupled with a request for forgiveness. Trust is hard to restore, but not impossible. Decide if a relationship with your family is worth the work if you're in this category. The world can be a mean place, and we all need people who love us, even those we have hurt deeply. I hope your family is capable of that love and forgiveness, if this is you.
If the alienating factor is instead an issue of lifestyle, e.g., gender and sexuality issues, political, religious, and values differences, or struggles with mental health, addiction, or finances, then your choice is different. Decide whether you will 1) educate your family further, 2) ask for targeted help from some of the most understanding family members in gaining the acceptance of other members, or 3) you'll instead merely agree to disagree. Whatever the case, calmly call out disrespectful behavior like namecalling and off-color jokes at your expense. Families need to respect one another, even if they don't like one another's views, or they disagree vociferously on lifestyle.
While you're going through this process, it's crucial that you rely on a positive reference group that can support you emotionally and socially as you are. If you are deeply troubled by the way your family has shifted you into the black sheep role, then do not hesitate to seek counseling.
I leave you with my favorite self-empowerment quote about knowing who you are: "No one can make you feel inferior without your consent." - Eleanor Roosevelt