Does a Federal Statute Ban Requirements to Use Vaccine That's Under an Emergency Use Authorization?

No, says, a July 6 Memorandum Opinion of the Justice Department's Office of Legal Counsel:

Section 564 of the Food, Drug, and Cosmetic Act ("FDCA") authorizes the Food and Drug Administration ("FDA") to issue an "emergency use authorization" ("EUA") for a medical product, such as a vaccine, under certain emergency circumstances. This authorization permits the product to be introduced into interstate commerce and administered to individuals even when FDA has not approved the product for more general distribution pursuant to its standard review process. Section 564 directs FDA—"to the extent practicable" given the emergency circumstances and "as the [agency] finds necessary or appropriate to protect the public health"—to impose "[a]ppropriate" conditions on each EUA. Some of these conditions are designed to ensure that recipients of the product "are informed" of certain things, including "the option to accept or refuse administration of the product." …

[We conclude that] the "option to accept or refuse" condition in section 564 [does not] prohibit[] entities from imposing such vaccination requirements while the only available vaccines for COVID-19 remain subject to EUAs…. This language in section 564 specifies only that certain information be provided to potential vaccine recipients and does not prohibit entities from imposing vaccination requirements.