I think another form of fear needs to be distinguished, which is fear that directly defends a bodily safety need
Imagine being given a hammer and a nail and told to hammer the nail through the palm of your hand. It is unlikely that you would be able to "push through" your fear of doing this. If you were in a room and told you wouldn't be allowed to leave until you hammered the nail through your hand, you would probably get more and more frightened and upset the longer you stayed in the room.
It is unlikely that breathing exercises and calm visualizations would help. It is also unlikely that being asked to explore why you feel your fear, or to explain what you imagine will happen when you hammer the nail through your hand, would help.
If your therapist kept prompting you to talk about whether seeing images of the crucified Jesus was causing you to associate nailing your hand with your negative religious experiences, or to defend why you expected nailing your hand to be painful, this would probably make you feel that your therapist fundamentally does not understand your feelings at all.
I think this kind of fear is a distinct KIND of fear. The imminent prospect of harm to the body causes fear that cannot be addressed through changing the afraid person's associations, cognitions, or behaviors, because avoiding harm to the body is a raw survival instinct.
Furthermore, being forced to actively participate in this harm to the body, that is, to behave as though consenting even though under threat of force or duress, removes the person's power to retain some sense of control by fighting back (even if futilely).
Isn't the Saw franchise about something like this? This type of fear is also very often utilized in torture.
Fear of rape or sexual violation evokes this "Saw trap" type of fear in the same way that pain or mutilation do. Therefore, a lot of the fear I experienced in my life was the "saw trap" type of fear: I feared doctors and medical environments because I knew from an early age that doctors touch your anus and genitals, and while I don't specifically remember this happening, I do know I had many, many experiences of completely non-consensual medical procedures: I became terrified of needles at 15 after getting blood drawn forcibly while i was crying and saying "no" repeatedly.
When I learned later in life that I "had to" get a pelvic exam (and was told by sexual health sources on the internet that I could not refuse), I viscerally understood this to be rape. Being told this was, to me, being told that I would be raped over and over again, in a context where I was not allowed to fight back.
This was a completely rational and non-distorted cognition based upon the knowledge I possessed. I had been directly told that I could not refuse, and I had experienced firsthand that I forfeited my bodily autonomy by going into a doctor's office. I did not have a single positive, respectful, or non-coercive experience with a doctor, so there was no reason to doubt.
My opinion is that "Saw trap" fear is completely different from anxiety because the fear is so fundamental, and it cannot be treated with typical therapies for anxiety: it can only be treated with safety.
In my case, that means: medical experiences that genuinely feel safe and genuinely feel driven by my own choices, and relationships with medical professionals who I can trust not to use force or coercion, who I genuinely feel will not do anything to my body that I did not first consent to.