Is dating a transsexual socially accepted?

By whom? Depends on your social circle otherwise no.
Social acceptance. Many people disapprove of transsexuals, as if they're in charge of dictating what others should feel. Transsexuals say they didn't choose to be in the kind of bodies they inhabit, and that they identify with the other gender. Depending on the importance of social approval to you, you may risk the same kind of social outcast feeling many transsexuals experience. It isn't rational, but does exist.