That’s quite a fair argument. National anthems and the direct participation of the military are quintessentially acts of a political nature.
Showing respect for one’s country is not a political act. At least, it never was in a country where people from both political parties equally loved the US.
Only in a country where a huge portion of the population does not love the country and refuses to show respect for it could the playing of the national anthem be considered a political act.
If that’s the country leftists like you have created, it’s more important that ever to play the anthem every opportunity there is, in order to, if for no other reason, identify potential enemies of the state.