A few months ago I emailed the Green Party because of concerns I had with harmful anti-LGBT views held by "Green Party Women". This is their reply if it's of any interest, they didn't specifically mention the anti-LGBT spin-off group but the reply suggests the main party are in favour of LGBT rights.
"Thank you for getting in touch. The Green Party is strongly in favour of LGBTIQA+ rights and strongly believes transwomen are women, transmen are men and non-binary identities exist and are valid.
Our liberation group, LGBTIQA+ Greens works to ensure we have strong LGBTIQA+ representation and helps shape our policy.
We have been working with external experts Diverse Matters, who conducted an audit of our party’s practices in respect to the Equality Act 2010 and wider best practice in regard to inclusion.
Thanks to this audit, Diverse Matters recently shared with the wider governance of the party a report suggesting an action plan covering policies, procedures and training. You can see the executive summary report here.
This report is now in the hands of our governance bodies GPEx and GPRC, who are working towards embedding and implementing these recommendations into our processes and internal party culture. We are also currently reviewing a number of other areas, including our safeguarding policy and disciplinary process to ensure they meet good practice for membership organisations.
In addition, we have a Culture Working Group which is working to promote a positive culture that reflects our values, and the rights and responsibilities chapter of our policies is being rewritten to ensure that all the protected characteristics are fully included.
With these and other workstreams there is a lot underway, which we hope will help build a safer environment for all and guarantee that our policy goes beyond our manifesto and constitution, and into our internal party culture and processes.
I hope that helps shed some light on some of the work that is going on within the party and you might like to read more here.
Thank you for your support."