While an older article
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Actually, no regulation specifies that the president should salute (or return the salute of) military personnel. In fact, U.S. Army regulations, for example, state that neither civilians nor those wearing civilian attire (both of which describe the U.S. president) are required to render salutes. The regulation states:
“The President of the United States, as the commander in chief, will be saluted by Army personnel in uniform.
“Civilian personnel, to include civilian guards, are not required to render the hand salute to military personnel or other civilian personnel.
“Salutes are not required to be rendered or returned when the senior or subordinate, or both are in civilian attire.”
Fact Check: Should presidents return salutes from the military? - News - The Florida Times-Union - Jacksonville, FL
I think anyone who is making an issue of this should be ashamed and look up what regulation require.