Sure, but neither side is presuming that emergency orders are (un)constitutional.

Both opinions do ultimately agree that emergency orders are, in general, constitutional during a pandemic. And not by presumption, but by an examination of the laws and facts.

That is why neither position makes this a central question: not because it's presumed, but because they both ultimately agree it's not a point of contention.

The point of contention is whether this particular order's treatment of churches is constitutional. Not whether the orders in general are constitutional.

Once both sides agree that the orders are in general constitutional, the argument that churches should be allowed to stay open while some other similar things stay closed now does require an argument.

There seems to be some very mild confusion here. An "emergency stay order" doesn't refer to an order to stay home during an emergency. It's a request to the court to ask for the enforcement of the law to be temporarily halted (stayed) for the reason that it will cause immediate or irreparable harm to the moving party (it will injure the religious establishments).

There's no question that such requests are generally Constitutional.

That is another good observation that was hard to understand at first to someone very familiar with law (like myself). It would be a very strong action for the supreme court to take action here. The dissent doesn't really say why it would be irreparable damage to keep churches closed a little bit longer.