In baseball, players do that all the time in free agency, and no one makes a peep about disloyalty.
So does his comment about treason, which plugs into the mentality of those accusing the President of sedition and disloyalty.
The whole state of Arizona may be under house arrest for suspicion of disloyalty.
early 15c., from Middle French desloyaulte, from Old French desloiaute, desleauté "disloyalty, faithlessness, marital infidelity," from desloial (see disloyal). Especially of allegiance to a state or sovereign since c.1600.