That’s a good point. What if the shoe was on the other foot?
However, I think that is unlikely due to the nature of conservatism, which accepts the co-equal branches and the separation of powers doctrine.
The issue here is not one court overruling another. The issue is that the courts (in this case the lower courts) are overstepping the limits of the judicial branch and venturing into the domain of the executive branch. It’s kind of like “legislating from the bench” - except in this case they are “executing from the bench”.
This overstepping behavior is a liberal MO, not a conservative MO. Luckily, the SCOTUS is behaving appropriately and disciplining liberals within its own branch. I’d like to see more discipline in this regard.
The president has to push the issue. It is his power which is being diminished and in this case it is dangerous for the country. We can’t have judges responsible for national defense.