It's honestly so bewildering to see so many people just openly admit to not understanding what is wrong with being anti-choice. It isn't because it's "disgusting" it's because it is harmful and it is harmful in a way that is specifically dependent on dehumanizing women. There isn't a person who is anti-choice who also has a fundamental respect for human life in dignity, these two things are incompatible.
So, yes, whether or not your doctor is capable of authentic empathy is actually pretty crucial to their ability to perform as a healthcare practitioner. Beyond just the reality that they're more likely to discount your pain and suffering due to this, they're also statistically more likely to actually intentionally harm groups of people they view as less than human (racism, sexism, transphobia, ableism, fatphobia). You seem to think the issue is that being anti-choice somehow indicates a skill-level for these tasks, that is an incredible lapse in empathy yourself there bud.
It is not an opinion to be anti-choice, it is a decision that shows your fundamental values and lack of moral grounding, which yes, makes you ill-qualified for any job where you have power over vulnerable people. Period.