No physician would proceed with a radical intervention such as amputation without extended consultation with the patient, likely involving an outside psychiatrist, or two or three.
Not all conservatives agree with you, as seen by the bills banning gender-affirming care, and not just for children either - at least four states are moving to ban/restrict it for adults over the age of 18.
https://www.cnn.com/2023/02/11/politics/gender-affirming-care-bans-transgender-rights/index.html
A lot of the more hysterical conservative discourse around transgenderism seems predicated upon the false assumption that you can walk into a clinic, pronounce yourself as trans, and get your junk chopped off that very afternoon. No, that's not how it works.
It starts with counseling, then soft (and reversible) interventions like puberty blockers and hormone therapy, and only after a lot of that does the option of an irreversible surgery ever get put on the table. Some trans people complete only part of the process and stop. Others choose never to get the surgery, even though they otherwise fully identify as trans.
It's time-consuming and expensive process, and some never get to the exact endpoint they want simply because of the costs of healthcare in America. And others sadly commit suicide because they can't get the care they need for some reason and can't bear to live inside their bodies.
I believe as a general principle that freedom means that people have total control over their own bodies, subject to appropriate safeguards like I've described above. After all, I support euthanasia. I don't see how anyone who supports the right to die under physician assistance would oppose the idea that same person shouldn't have the right to amputate a body part that they feel like they can't live with.