Run2468, I applaud you and your team for the stance you're taking and the reasons behind it, but I do agree with PPs that some of the language you've used to soften your statement and to appease your critics also serves to make your message less clear.
For example, in the two sentences:
"I am open-minded to the suggestion that this 12% statistic represents an underlying transphobic attitude, which is unacceptable. However, asserting a right to a female-only space is not in itself transphobic and is legally protected."
the first sentence appears to undermine the second. When you say you're "open-minded to the suggestion", this implies that you think this might be the case - but if it's not inherently transphobic to want to compete against just other women, then why would you countenance the notion that this 12% might just be transphobic?
The rest of your statement suggests that you suppose that these 12% of women simply want a female-only experience, which is understandable and completely justified, as evidenced by the fact you're providing it to them, and by the fact UKA advises the same.
There was no reason to agree that they might just be transphobic, and I don't think that line was helpful in any way.
Other than that, though, well done for upholding women's rights and for standing your ground!