Not so much.
Executive orders can impact any entity that receives money from the executive branch. (Medicare, Medicaid, Tricare, CHAMPVA anybody??)
For example, as a DOD contractor, my company is required to comply with Executive Orders on classified material every day.
Of course, we wouldn't have to comply, but then we would forfeit competing for DOD work. Likewise, I'm sure physicians would be able to not comply, but they may end up forfeiting the ability to accept federally funded health benefits.
Many doctors are setting up cash only practices. They don't accept any sort of insurance. That seems like the way to handle this situation. Of course, hospitals and their staffs are another matter.