The default principle—that someone is free to do what he or she desires in the absence of a compelling reason why he or she should not—may make it possible to resolve ethical disputes without recourse to a particular moral framework.
AMA J Ethics. 2015;17(4):289-296. doi:
10.1001/journalofethics.2015.17.4.spec1-1504.
Instead of succumbing to the urge to portray cultural differences as a dichotomy between clashing opposites, we should endeavor to note our common humanity, acknowledge the plurality of viewpoints within a given culture, and appreciate that cultures can evolve without being untrue to themselves.
Qualifying conscience protections for institutions with requirements that they minimize hardship caused to the patient would prevent religious institutions from acting as a choke point on the path to services.