@LadyHester I'm currently working with my daughters' school to help the school to navigate how gender identity is taught. Unfortunately, it's an absolute minefield of different stakeholders with completely different viewpoints and motivations. However, I have found a pathway through it. Obviously I'm just a parent so all of this is being taken at the school's pace but I'm happy to share if it's helpful.
This all started off with me focusing on just my daughter's EHCP (there are some older threads about that I can dig out if they are of interest to anyone), moved on to a review of the PHSE/RSE materials and we're now at the stage where I've got some interim guidance that is already in place in another local authority (thank you to the MNer who shared this if you're reading this) and it's currently all going through the senior leadership/governor route.
The biggest problem in the RSE/PHSE materials was the conflation of sex and gender and the way that this is slowly introduced to the point where it's easy to miss what has happened. There's loads of information on Safe Schools Alliance and other similar sources (Transgender Trend for example) that helped me to review it.
The best way that I have found to progress my discussions is to focus on the fact that gender (identity) is a belief. I've seen this mentioned above too in other comments. Some people believe that we all have a gender (identity), some people don't. Unfortunately by introducing the concept of gender as a fact, as a social construct that differs from sex, it signposts children towards the belief that they have one.
I've posted a screenshot from something that I've written for the school which helps to show how I've been positioning it. As frustrating as it is to position my own views on this as a belief, I have accepted that the people who believe in gender identity hold it as a truth. Just as I hold sex immutability as a truth. In reality, I suspect most people who believe that we all have a gender identity do so because they've been introduced to the concept as a universal truth. So in short, I don't challenge the principles of the belief, but I challenge it being taught as a truth and I challenge the impact that this compelled belief has.
@Pieceofpurplesky I totally get where you're coming from by separating sex and gender. Building on what @MargotBamborough has said, unfortunately I still think that this signposts children towards the belief that we all have a gender identity. However, by separating them out as you've done, it does afford an opportunity to explore the alternative belief that sex is immutable. If I were a teacher I would personally focus on getting backing from the school that they understood the law in relation to the Maya Forstater judgement before I went ahead with this.
In the screenshot below, the DSD link is the NHS page and the "protected in law" one is to the EHRC page which covers the Forstater judgement. The others are self-explanatory I think.