AJ4DW: "Please feel free to bow to Washington three times a day and recite such an oath, that's your privilege, but when you force me to do it you're infringing on my personal rights."
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This is where you are wrong, if armed men came to your house and forced you to recite an oath that would be infringing on your personal rights. If you choose to join an organization that requires an oath, then your options are give the oath or don't join.
This is a major reason why many volunteer groups don't get respect, you want to play in someone else's game, but you want to play by your own rules. The rules are there, and they are there because the people who's careers are on the line if things go wrong made them, either agree to play or don't.
Don't like the rules then find some way to help indirectly, one role EmComm plays requires no served agency, that is Health and Welfare traffic, get your group and set up across the street from a shelter, or some other common area and offer the public to send out messages to tell relatives outside the area they are OK, this is an underused service we offer that many served agencies have no want to do.
But if you want to be in the shelter, or a fire station, or shadowing the mayor, or anywhere else another agency is in charge.... expect there to be rules, expect some to be silly or stupid, expect to disagree with some of them, but understand you must follow them or you will not be welcome.