"Brandon and Braga" are one person (regular Star Trek writer Brannon Braga) I think you mean (Rick) BERMAN and Braga.
I'm not sure about Braga's political leanings (I would assume liberal, like most TV writers) Berman's certainly liberal-- one time during the run of Star Trek: The Next Generation, he angrily remarked at a press conference that Star Trek would never do any show that would portray an "anti-choice" abortion message on the show.
True, they've eerked a couple of liberals in the past couple years, but I think this is more because of their LACK OF SPINE than anything else. For years, they've been telling the gay lobby they would include an opening gay cast member, but haven't delievered. I'm sure they like the idea personally, they just feel it would be suicide for the ratings (and they would be right)
The only time I've heard of a conservative message on ST in recent years is some liberals were ranting and raving that "The Expanse" episode of Enterprise was propanda for George W. Bush's Iraq policy. Conservatives really didn't see this, and the I doubt the episode was written by Berman or Braga anyway.
Truth be told, Star Trek was more conservative-leaning in the 80s under the Harve Bennett/Nicholas Meyer duo. Watch Star Trek II or Star Trek VI and you won't see any touchy-feely politically correct stuff. And then there's the original stuff under Roddenberry. He leaned left on the few things, but I always found him more libertarian and than liberal.