Personally, I'd quietly approach HR and explain that being LGB, I find Stonewall homophobic and hostile to LGB people, explain about the LGB Alliance split and its reasons, and that I had serious concerns about the inclusiveness or safety of LGB people in Stonewall's 'vision'. And that I'd have to think very seriously about continuing to work for an organisation 'allying' itself to homophobic politics. But purely from the point of view of concern for your workplace I'd be quietly mentioning to a manager and/or HR:
There has been an assumption this far that Stonewall are like the National Trust or the RSPB or Great Ormond Street: the government supported, national institution of objective, neutral experts on their subject, and they have held that level of public trust. They also have nice shiny plaques etc to stick in the front lobby like other neutral groups who do workplace qualifications around healthy eating/ quality assurance/ etc etc, and so look like just another approved demonstration of quality. It has to be made clear that you might as well commission training intended to form policy by Green Peace or Momentum; it's a highly partisan political lobby with a specific agenda. It does not comply with current British Law and seeks to overturn it by influencing policies and practice via their training. (This can be easily evidenced.) This leaves the organisation potentially vulnerable to legal proceedings.
Due diligence must be carried out on the trainers to ensure that they are actually qualified to speak and advise on subjects that involve the Equality Act (ie training and qualifications in ALL groups under the EQA, not just transgendered people) and safeguarding, as trainings have been carried out where this has not been the case. (This can be easily evidenced. Not to mention as far as I'm aware there is one person who has delivered such training currently under investigation and another having been declared 'incapable of understanding safeguarding' by an inquiry.) Setting up policy around one specific group without equally considering ALL protected groups and the impact upon them may break the law and leave the organisation open to legal proceedings. It may also be highly embarrassing for the company if in the future the trainer or policies turn out to be connected with a safeguarding/ethics issue.
Many organisations have standard principles of not 'allying' with any one political point of view, and have been innocent to the fact that when inviting Stonewall training they are doing so. Will the company openly 'allying' itself to be compliant with and representative of a specific political position be something they would deliberately choose to do? Might there be possible consequences to consider first?