The simple observation that people who identify as trans exist is not an ideology.
But physical sex also undeniably exists, and whatever trans people believe about their gender, it is not the same thing as physically being the opposite sex. Obviously.
The ideological aspect is not how trans people feel about themselves. It is the extension of this feeling into the claim firstly that all humans have an innate gender that is separate to their sex, and secondly that it is this inner mental gender that makes one really a man or a woman, and therefore it is this rather than the practicalities and challenges of our physical sex and how society and individuals react to it which is the significant factor in sports, in privacy, in sexuality, in sexual abuse, in VAWG, in sexism and in unconscious bias against women, and that all the protections, rights and opportunities put in place for women are correctly accesible to anyone who simply claims their inner gender is Woman, while physical sex is mostly irrelevant and can be ignored in any context beyond the immediate needs of the body. THAT is the ideology.
The undefining of female reality, the denial of female experiences of sexism within patriarchy and the rebuilding of society to center gender identity is a belief system that goes way way way WAY beyond simply recognising and accepting the existence of trans identifying people.
If TRAs were advocating that trans identifying people be accomodated alongside the reality of sex, without denying women's sex-based oppression and without appropriating women's sex based rights, protections and opportunities, I'd be right there fighting with you.
But promote a regressive, sexist ideology that can look at the history of female lives and tell the bare faced lie that our bodies do not have consequences, that can straight faced claim on the one hand to be somehow "feminist" and on the other believe that men and women just have different types of mind, and that something in a man's mind can be so unmanly he is actually a woman, and try to make us believe that this is challenging the patriarchy? Yeah, I'm never going to think that's ok.
Female people exist in our own right outside the imaginations of men. Our challenges and needs don't go away just because some men see our lives as metaphors or refuges from things they want to reject in themselves.
Any ideology that denies this basic truth is deeply sexist, regressive and patriarchal and we should reject it completely.