Unstable partners happen all the time, and those that project issues of fidelity are either cheaters themselves or they fear losing your or have abandonment issues, so they hold on tighter with gaslighting routines.
Be kind, help those that you state, and then when in private go back and have a discussion. Even though I know it isn't easy either confront it and move on, or if you can't and your personal sanity is at risk. Step away from the relationship (do note I don't recommend ghosting but I get it)
One thing you could say is, you keep stating I am going to cheat, what gives you that impression talk to me about your fears.