I think there’s a lot of misinformation around on Labour’s stance.
Yes, they want to make it easier to get gender recognition certificates (which is also something the Tories did about 3 years ago) by dropping the 2 doctor requirement in favour of 1 doctor. Bearing in mind that very few GRC’s are applied for (usually around 30 per year) and around 95% of applications are successful, I’m doubtful that Labour’s changes would result in an increase is successful applications.
Some people have raised concerns about Labour potentially scrapping the spousal “veto”; I can understand being opposed to that but it’s an incredibly minor issue to me. The “veto” has only been exercised twice in the nearly two-decades since the Gender Recognition Act came into force (and no idea if by men or women).
Labour have said they support the existence of single sex spaces and will implement the recommendations in the Cass report.
I’m not quite sure on is the interplay between implementing the Cass report with their pledge to band trans conversion therapy, thought I don’t think those two things are necessarily incompatible depending on how conversion therapy is defined. The conservatives have also said they’d ban trans conversion therapy.
The only real difference that I see between the two is that while Labour are promising to provide legal guidance on the application of the current Equality Act, the conservatives are (now) pledging to amend it to define sex as biological sex. I can understand that the Tory stance is more appealing to some but it would be fraught with legal challenges, which is presumably why they’re now only making the pledge (after years of inaction) when they know they are not going to be in government anymore.