I'm sorry you encountered this, OP, and I completely understand that it is a barrier to accessing the support that you want and are entitled to.
Any questionnaire that asks about 'your pronouns' is unnecessarily taking sides in a contentious social issue that is recent, irrational, and probably temporary.
Any health questionnaire that asks about 'your pronouns' or 'gender' but not about your biological sex is missing out a vitally important piece of medical information.
I recently got an information pack about planning end-of-life care. It asks about pronouns and gender, but not sex.
I had a similar reaction to the OP's - a mixture of
'Oh FFS!'
and
'How can I trust these people to treat me properly and respectfully if they can't even acknowledge that I'm a biological woman, or that the category 'woman' is biologically defined and of medical significance?'
I understand that it's a barrier, OP. You don't want to be seeking support from people who clearly don't accept how you define yourself, i.e. according to your biological sex, and what position you take on this social issue.
I'd feel the same. A therapist who indicated that they believe that some men can become women, or that we must all act as if some men can become women, is not somebody I'd feel I could trust.
I hope you get the support you need, without having to slalom through ideologically-motivated practices.