Wasn't it Congress who passed 5 U.S.C. § 7311. which says a person may not “accept or hold” a federal job if they “participate in a strike” against the U.S. government.

https://www.law.cornell.edu/uscode/text/5/7311

originally passed as

https://uscode.house.gov/view.xhtml?edition=2023&num=0&req=g...

So arguably if Reagan had not fired them he would be failing to uphold the laws of the United States.