If illegal aliens and congress don’t have to take it.....why should anyone?
This should be part of their argument—equal protection/unequal application of the law/mandate.
That's the real point.
By the very nature of the order it is arbitrary and capricious rather than reasonable. You can't make the case that universal vaccination is required because it is a medical emergency and the exclude large classes of people because it is politically expedient.
The fundamental rule of any executive action is that it must be "reasonable" in light of the facts supported by logical reasoning to reach the executive decision.