In this article, I address what kinds of claims are of the right kind to ground conscientious refusals. Specifically, I investigate what conceptions of moral responsibility and moral wrongness can be permissibly presumed by conscientious objectors. I argue that we must permit HCPs to come to their own subjective conclusions about what they take to be morally wrong and what they take themselves to be morally responsible for. However, these subjective assessments of wrongness and responsibility must be constrained in several important ways: they cannot involve empirical falsehoods, objectionably discriminatory attitudes, or unreasonable normative beliefs. I argue that the sources of these constraints are the basic epistemic, relational, and normative competencies needed to function as a minimally decent health‐care professional. Finally, I consider practical implications for my framework, and argue that it shows us that the objection raised by the plaintiffs in Zubik v. Burwell is of the wrong sort.