You can see the dissenting opinions of Justices Alito, Gorsuch, and Kavanaugh here; Justice Alito’s opinion is joined by Justices Thomas and Kavanaugh. The Justices in the majority (Chief Justice Roberts and Justices Ginsburg, Breyer, Sotomayor, and Kagan), who decline to issue an injunction pending appellate review, haven’t written an opinion (though note that injunctions from the Supreme Court pending appellate review are extraordinary remedies). But you can see the District Court opinion, which the dissenters would have blocked, here.
From Justice Alito’s dissent:
The Constitution guarantees the free exercise of religion. It says nothing about the freedom to play craps or blackjack, to feed tokens into a slot machine, or to engage in any other game of chance. But the Governor of Nevada apparently has different priorities. Claiming virtually unbounded power to restrict constitutional rights during the COVID–19 pandemic, he has issued a directive that severely limits attendance at religious services. A church, synagogue, or mosque, regardless of its size, may not admit more than 50 persons, but casinos and certain other favored facilities may admit 50% of their maximum occupancy—and in the case of gigantic Las Vegas casinos, this means that thousands of patrons are allowed.
That Nevada would discriminate in favor of the powerful gaming industry and its employees may not come as a surprise, but this Court’s willingness to allow such discrimination is disappointing. We have a duty to defend the Constitution, and even a public health emergency does not absolve us of that responsibility.
And from the state’s argument against issuing an injunction:
[G]aming establishments face numerous additional restrictions and regulatory oversight not faced by houses of worship, making them dissimilar activities. Failure for gaming establishments to follow the Emergency Directive risks significant punishment. There is no comparable basis on which non-compliance can effectively be enforced against a house of worship. Instead, houses of worship and other entities impacted by Directive 021 are subject to enforcement by local law enforcement, subject to their prioritization of resources.
Choosing to reopen a highly regulated industry, that is subject to significant regulatory control that allows for a rapid shutdown if a second COVID-19 outbreak arises, makes sense. This policy determination warrants deference from a court, as “[o]ur Constitution principally entrusts ‘[t]he safety and the health of the people’ to the politically accountable officials of the States ‘to guard and protect.'” Under these temporary circumstances, Nevada is entitled to deference on its regulated, limited reopening of gaming establishments.
There’s a lot more going on here, but I’m afraid I don’t have the time to post on it now; if you’re interested, have a look at the opinions, and the parties’ filings.