the way that they don't engage with any other opinion, like it's not allowed, how can that be progressive?
It isn't. Either you believe in valuing and listening to all people fairly irrespective of their characteristics, and the power of debate and winning arguments on their merits, or you believe in only supporting the rights and equality of groups you personally think are of value and forcibly shutting up everyone else.
If you believe that Terfs should not be allowed a voice, a vote, legal rights (or if you believe Twitter, to even be allowed to live) because of their views, then you believe X should not be allowed civil rights because of their Y characteristic. So Tories should not be allowed civil rights because they vote Tory. People worried about immigration should not be allowed civil rights because they are bigots who vote in a bigotted way. Terfs should not be allowed civil rights because they keep terfing even after they were told not to.
Go back 100 or 200 years and put 'black' or 'Jewish' where X is and you see how progressive that view really is. You would also think that having destruction tested calling people worried about immigration 'bigots' (publically in Gordon Brown's case), shouting at them for having stupid opinions and completely blanking them as beneath contempt instead of listening, engaging, explaining, putting enough genuine light on it for everyone to see the reality, the political body would realise it doesn't work. It was one of the big factors that led to the unholy mess of Brexit.
Labour have to go back to being able to debate, to explain, to actually win arguments and talk about the really difficult things without shame and blame. The arguments stand for themselves if they're good enough.