I am not saying this because I agree with it, but because I know this is the argument the court would make, and I ask that anyone who replies keeps that in mind. The argument would be that skydiving is not a belief or standing of a recognized religion. Thus, abortion violates freedom of religion under the first amendment, but skydiving does not.
Now, that’s all stupid because a doctor should have to set aside certain rights, including the ability to discriminate in any way against providing medical care as per their oath, to take the job. There are a variety of other arguments against the stance, but skydiving is not on the same level as abortion when it comes to religious rights. Maybe a Muslim doctor refusing to treat a patient suffering from gastrointestinal distress from eating pork?