It makes sense from a separation of powers standpoint. This comes from an executive order, and the president cannot order Congress to comply.
Care to chime I'm on the CDC, FDA, and Chinese students.
The executive order requires vaccines for all employees except to the extent prohibted by law:
"I have determined that to promote the health and safety of the Federal workforce and the efficiency of the civil service, it is necessary to require COVID-19 vaccination for all Federal employees, subject to such exceptions as required by law. ,,,
Each agency shall implement, to the extent consistent with applicable law, a program to require COVID-19 vaccination for all of its Federal employees, with exceptions only as required by law."
An executive order can't invalidate or contradict enacted law, so that exception is required. It will probably take the agencies a little time to figure out what the exceptions are - e.g., assuming someone can claim a religious exception when that will be granted. There are always fights on the edges of these policies, but the central thrust is as broad as you can get.
https://www.whitehouse.gov/briefing-room/presidential-actions/2021/09/09/executive-order-on-requiring-coronavirus-disease-2019-vaccination-for-federal-employees/