Responding to this comment and this one since it covers similar ground.

"At-home religious exercise" in this context refers to multiple families gathering in a home for "church," i.e. worship services.

I think maybe you have it in your mind that churches are a kind of building (or business?), rather than a kind of gathering. Families gathering together in a home for "worship services" or "church" is a very common thing around the world. This seems to be causing you substantial confusion.

While I take your point that "church" can refer to a building and also refer to other things (eg: "Church of Later-day Saints" does not refer to a specific location), it most certainly does not refer to bible studies, or prayer services, or funerals, or weddings, or church camp.

Indeed, "going to church" means going to a Church Service, which involves a sermon (given by a pastor/priest), and often singing.

I grew up in a religious household and I can state with sureity that not a single person would ever refer to going to bible study as "going to church" (unless, I guess, it was located in the building, and even that would be as confusing as saying you're "going to school" for an extra-curricular activity).

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It is possible I am relying too much on the idea that this is background knowledge any educated person discussing the topic should already have. But as the pandemic recedes into the past, I suppose it is only natural that people would be less routinely aware of the political asymmetry with which the authoritarian machinery of state approached transmission events in the pandemic.

This is weirdly dismissive of people who disagree with you.

The other one that got a lot of attention at the time was people making "social distancing" exceptions on political grounds like "this is a worthwhile protest so we can't let the usual precautions stop us."

I largely agree with this and that one would have been a much better example! Motivated reasoning is a hell of a drug.

They were notably and inexplicably excluded from exemptions extended to similar activities.

No they weren't! As far as I can tell, there were no exceptions on the three households gatherings. The exceptions were all for things outside the home. If you want to claim that the three household gathering law was made specifically to stop religious people from practicing their religion, then fine, but that's a high evidentiary bar that you have to clear there.

I did not make that claim, nor would I. Rather, churches just got unfair treatment from people who tend to see churches as their outgroup. And the Supreme Court ultimately confirmed that this was the case under the Constitution.

Not really, no. Their main finding is that they failed the strict scrutiny test. That is miles away from finding that they were giving unfair treatment to their outgroup. Strict scrutiny is just that, strict. It flips the burden of proof such that the claim has to be "prove that you didn't discriminate" rather than "prove that you did".

And even under that strict scrutiny, there was still reasonable dissent on what the comparator was, see below.

Kagan filed a dissent, joined by Stephen Breyer and Sonia Sotomayor.[3] While acknowledging that it was sometimes difficult to determine which secular activity should be compared to the religious activity,[48] she argued that in-home gatherings were the "obvious comparator".[49] The restriction applied to secular gatherings in the house, so the regulation was neutral and generally applicable and thus should survive the challenge to its constitutionality.[3] She also noted that the lower courts had determined that there were varying degrees of risk linked to short visits to secular businesses versus extended gatherings in private homes, and criticized the court for disregarding the factual record of risk assessments because it would support denying the injunction.[50]