I would like to see some reliable polling on this issue (and other related issues).
Well, Pink News did some (18% support for self ID by YouGov) and Wings Over Scotland did some (25% support for self ID by PanelBase).
We're waiting for the results of Helen Staniland's YouGov polling on male bodies in female spaces plus freedom of assembly vs hate speech (6 questions in all) which we all crowdfunded for last week.