Yup, I think that's completely true. People even who are shown often think the instances of things like transwomen causing problems in prisons are flukes. And to be fair, we know that bad mistakes and flukes do happen in lots of systems and they don't always mean that the underlying way of doing things is the problem.
People are also aware that things they are told through the media may be factually incorrect or slanted. So when they hear something that seems just unlikely or crazy, they assume it's biased or bad reporting or some such.
In terms of the science of gender, or the psychological medical element, they don't feel expert enough to debate what seems to them to be a consensus.
With sports, many people know enough to be a least suspicious of the idea of transwomen competing on women's sports - they've been involved in sports themselves for example. And they also know that the whole concept of sports competition is based on the physical body. So they question.
And then if they see it, they are hit in the face with it.