To be honest, I don’t think the majority doesn’t have a problem with GA and PM. I think the majority doesn’t know and doesn’t care about Gillian’s personal life. They probably would care a lot more if she was with David, tho.
I do think she’s damaging her image inside her fandom. She probably gave a few thousands of views on the trailer of The Crown but at what price? No one likes to tweet and get 90% of negative replies or people making fun of you. So of course, it’s a tiny tiny part of her audience and in the end, it’s a drop in the ocean. But it’s also a dangerous ground. What do you think will happen when she keeps doing that over and over and gets more and more hate and more and more people making fun of her? One day, The Daily Mail, or any other brilliant newspaper will pick it up. I can see the headlines already. “what is happening with Gillian Anderson?”. They will publish the funniest and meaniest replies to her 50th tweet for a show she doesn’t play in, they will wonder why she’s doing that and happily remind us all of Portofino, they will shine a new light on all the shit that happened in the past year, and they will do it at the right time, like during the promo of XF for example.
That’s when her image won’t be ruined only in a tiny fringe of her fandom but for everyone else. When shit hits the press, it’s another story and it will if she keeps promoting this show no other obvious reason than sleeping with its creator.