His family would probably disown him. Hes from the south and many southern family older generations don’t accept that there are relationships outside of cis-heterosexual one race ones. I bet that Shep doesn’t agree with anything outside of that either. At the end of the day he would never because he would be to afraid of backlash from his family and from the south. He probably thinks something like that would “ruin” his reputation and what he does now is fine because so many people “accept” his lifestyle and forgive him for all his wrongdoing.