It would just be nice to have parity. Stonewall are welcome to flog their own agenda and message and deal with any consequences that may arise from misrepresentation. But if that organisation is going to be involved then the LGBA also needs to have equal input, as Stonewall do not represent all LGB people in their TQ+ focused agenda, there are aspects very questionable that need to be considered by someone lobbying for LGB interests in their own right.
If TQ+ political lobbies view this as a threat to themselves, then that's quite interesting in what it says about their views, their impartiality and true good faith in representing all LGBT people (as opposed to the ones who are useful to their agenda) and what they are aiming to achieve.
Likewise if Stonewall et al are consulted in anything, it should be automatic that grass roots specific women's groups are consulted, such as FPFW, KPSS, and others. The needs, views and issues of women should be independently consulted on, heard and taken into account. Again, if TQ+ political lobbies view this as a threat, then it has to be asked why they want to be the mouthpiece for women, control the narrative and prevent actual women being heard from. And why they are afraid that those voices would damage their political agenda.
It's why really the minister brief for equality needs to be broken back into its individual composite parts with one minister per group, who will represent that group's voices and interests . It would prevent the possibility of a well funded lobby group arising with less than shiny intentions, who had the power to subordinate and harm the other 8 characteristics to further its own interests. You know. Should that ever happen.