The opposite. There is a hypothesis that, by quarantining everyone with symptoms, the milder asymptomatic versions are allowed to spread

Not sure where you are but in New Jersey everything in the state is shut down, not just to people with COVID symptoms

This is a really interesting question that I don't pretend to be an expert on.

It probably comes down to what causes the difference in reaction to the infection. It could be that there are differences in people's immune systems that cause them to have a much more severe reaction. In this case the quarantining wouldn't have an effect.

If people who are having a much more severe reaction are getting a strain of the virus that has mutated to cause these more intense symptoms then you would see the issue you are talking about.

My uneducated guess is that it is the former, but I'm really not sure.

The opposite.

From the evolutionary point of view, a virus has no interest in being deadly: if it kills its host, it can't reproduce itself.

When social distancing (quarantine and lockdown) is enacted, it is harder for a deadly strain of the virus to reproduce and hence survive, as we react to it by putting into place stricter countermeasures. Which strains will thrive? The ones that able to "sneak around" unnoticed, by causing only mild symtomps.

I hear this a lot, but isn't evolution trial/error? Just because we can say it's not in an organism's evolutionary interest to evolve a certain way, doesn't mean it won't "try" it - at any stage in it's evolution. Also I don't think an organism has any active role in deciding what mutations occur, regardless of it's interest.

Are you perhaps misunderstanding something? Everybody with confirmed symptoms should be in quarantine, which you do from home unless you are so sick as to need hospital care.

Perhaps the more deadly strains are infecting people in hospitals (health care workers and other staff and patients)

Best way to test that would be to use different countries' death totals over time, and compare that to differences in quarantine policy.

By the way, you misspelled "quarantine".