https://www.pewresearch.org/fact-tank/2017/11/08/transgender...
There's a name for the phenomenon: https://en.wikipedia.org/wiki/Pluralistic_ignorance
For details on that distinction and attempts at consensus-building for the terminology, see https://journals.physiology.org/doi/full/10.1152/japplphysio...
In software development terms, this topic has no ubiquitous language.
In relation to your comment, their belief is not based in a shared reality.
It is one thing to ask people should be able can use a bathroom, and another to ask questions about personal sexlife and behavior. i.e. if you asked people if you consider transwomen equally with women at birth as sexual partners, I bet the numbers fall through the floor.
https://journals.sagepub.com/doi/abs/10.1177/026540751877913...
https://www.google.com/amp/s/www.psychologytoday.com/us/blog...
There are a lot of women I would not want to sleep with. Does not mean I question their gender.
Most heterosexual men identify as being attracted to women, and don't hold trans women in that category.
You could ask whether there is a study to assert parent poster's assertion, too. All I could say is that the burden of proof seems to fall on you with your statement, but most would take parent's at face value.
I'd wager that most people believe this. Not just feminists.