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.
To participate in a lethal injection is to occupy the medical role and use medical training for a purpose that is not part of the goals of medicine and that harms the recipient of treatment.
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.