I am going out with this guy and I feel like his parents don't trust me much. Should I break up with him?

I know it's not his fault but should I because I really don't want to be in a relationship with a guy whose parents don't trust me. Sometimes I feel like his parents don't like me. They even read the letters he sends me and then they keep them. I really love him a lot but they come on every date with us!!! Talk about NO PDA!lol