I think Alito went out of his way to indicate that it did not serve a compelling government interest. He said that the government has provided millions upon millions of exemptions, to include exemptions simply to health insurance plans that have been grandfathered in. All of these plans have zero requirement to provide this contraception coverage.
He outright says the opinion assumes that the issue in the case, providing abortificants, does serve a compelling government interest. That appears at point (c) in the Syllabus (but NEVER trust the syllabus). Attributed to Alito and the majority:
Under RFRA, a Government action that imposes a substantial burden on religious exercise must serve a compelling government interest, and we assume that the HHS regulations satisfy this requirement.I don't take that as agreement with the premise, beyond "assume for the sake of argument." The majority's focus is on the "least restrictive means" requirement, and it is failure on that prong that results in the abortificant mandate being against RFRA.