This can be very difficult because ultimately you want your family to approve of the person you are seeing.
The first thing I would do is have a mature conversation with your family and figure out what it is about them that they do not like. If something comes up that is a misconception, you can calmly address it without fighting. I think it is really important to remember that you shouldn’t be fighting during this conversation because you want to show your family that you are serious about this and that you are willing to hear them.
Secondly, I would try keeping your SO away from your family if the issues really can’t be resolved (ie they can not get over different aspects- religion, gender, race, etc). They don’t have to approve of your SO (as much as we want them to). It might be really hard to keep these two “lives” separate but it is do-able. This can really eliminate tension and stress between all parties involved.
Lastly, you family loves you and cares about you so I would hope above anything, they would just want you to be happy. But always remember that you don’t need anyone’s approval. Live your life how you want to live your life and do whatever makes you happy.