It is difficult when parents who love you are trying to protect you but at the same time this protection feels very limiting.
I think it might be time for you, your mom, and your dad to sit down together. Trying to solve this on your own will be too frustrating. Ask to have a meeting with your mom and dad and explain to them your struggle — that you want to honor them but you would like to give it a chance with your boyfriend. Bring the problem to them rather than away from them. Move toward the conflict, not away from it.
Ask for their help. Tell them the idea of just cutting the relationship out altogether puts you in a very bad place. Ask them to help solve it with you. Often this can lead to some shift in the stalemate.