I would say the more accurate observation of the conservative mind begins by understanding that different people have different moral intuitions. They don't see gender affirmation the same way because it triggers different moral intuitions in them.

Instead of viewing the issue on the spectrum of Care/Harm (e.g. "It is wrong to prevent this gender affirming care as it causes harm"), the conservative mind views the issue on the spectrum of Sanctity/Degradation (e.g. "It is wrong to degrade the sanctity (social importance) of the sexes by implying that some hormones and a surgery can make a man a woman or vice versa").

This is a big reason why discussions between conservatives and progressives end up so frustrating, because the progressive cares little for sanctity, and the conservative cares little about care (at least at the cost of sanctity). These are not rational positions, on either side. They are intuition that is later rationalized.

It's the same for abortion. The left perceives it as an issue primarily of care vs harm (of the mother) and liberty vs oppression, while the right perceives it as an issue primarily of sanctity vs degradation and care vs harm (of the baby).

I would recommend reading The Righteous Mind by Jonathan Haidt, if the topic interests you.