Decanter, IME transwomen who have gone through complete transition are the most likely to understand why the current agenda harms women. Many of them have been quietly using women's facilities for years, without incident. It's not in their interest either to permit just any male person who says he identifies as a woman into these spaces. It puts us all at risk. Would it help to know that there are transwomen who are against the direction current discourse and laws are heading?
There has been a big shift in the last few years and now the vast majority of people who identify as trans have not had surgery. I don't blame them for this. Surgery is a massive, lifelong commitment and the results are often not great. If people can get by without it I think that's a good thing.
There has been a cultural shift though - trans no longer means what it used to mean. Gender is now purely a feeling in some people's heads and is totally separate to their bodies or how they feel about their bodies. So we get things like 'female penis' and 'non-binary'.
If you sign but don't share your friend will never know. If you do share, you probably will get some flack, but not necessarily from your trans friend. Don't assume you know what her views will be just because she is trans. If she is in favour of anybody who identifies as a woman being treated as female for all intents and purposes, why are you worried about hurting her feelings? She obviously doesn't care about yours.