BJ knows exactly what he is doing.
My guess is that they are more worried about the stranglehold a lobbying organisation has on decision making. The influence lobby groups, not just Stonewall, have on Government has long been predicted to be the next big scandal.
My guess is that Stonewall's overreach is very convenient. This can addressed by tightening rules for all lobby organisations (including those who employ former Tory and Labour PMs.)
90 odd percent of the British public will oppose having natal men on female hospital wards, prisons, sport etc. The vast majority will oppose giving life altering drugs to young healthy, but possibly confused, teenagers. Most will support the idea of a charity that works to protect same sex attracted people. And equally will think that Sussex students, with the opportunities thay are being given, are very wrong to attack Prof Stock.
This is not about Labour or Conservative. This is about people being one, or all, of: sensible, scientific, concerned about safeguarding and protecting the vulnerable, and socially conservative.
The Conservatives are wary of being caught on the wrong side of any LGBT debate and being labelled the nasty party. Initally it was just backbencher David TC Davis MP who put his head above the parapet and received complaints and more. Stonewall continued overplaying their hand, and BJ has a strong majority. Liz and Kemi have tested the waters, following in the footsteps of Maya etc. Keir has managed to look silly and weak by espousing Labour's pro Stonewall line. Time for BJ to wade in and say what almost everyone is thinking.
Like him or not, it is good when any politician pursues sensible policies that reflect public thinking. More bizarre that Labour, along with a whole raft of major private and public organisations, cannot manage this.
I dont think Carrie is "pro Stonewall". I am sure she, like most people, opposes discrimination, whether against LGB and T people, women, the disabled, people of different races, religions or creeds and so on. Stonewall's agenda has been more than that. Seeking the prioritisation of one group of the needs of others. I think it was a masterstroke to have Carrie, who is not a member of the Government, speak at the Stonewall meeting during the conference. The Tories avoided having LGBT issues dominate the headlines, and Carrie very much focused on the LGB.
One redeeming feature of BJ can be that he is lazy, and relies heavily on advisors. Whoever in No 10 is advising him on this is clearly onside.