I don't understand this strategy. Dueling circuit courts of appeals? I thought an overruling would have to come from a higher court which would be Scotus.
Biden administration asks federal appeals court to immediately lift pause on business vaccine mandate - CNBC - https://archive.ph/1Q8kn
I'm no expert, but this is in fact a common reason for the supreme court to weigh in. Multiple cases for similar law conflicts with different outcomes.
Now I'm not certain that another circuit court can overturn the injunction nationwide, but I'm sure that won't stop the commies.