Eh… I see where you’re coming from, and I’m generally against homeschooling as well. For various reasons, I wish I hadn’t been and wouldn’t do so for my child.
That said, I’m inclined to disagree. It only promotes what the parents put into it - which, yes, often is a lot of religion, but it isn’t intrinsic to the practice. The religious component I suspect is where you get the stunting of open-mindedness and critical thinking ideas, but fwiw I and several of my siblings have since left the faith for atheism, and even those who still participate in religion are mostly rather progressive. I do fully recognize that I and my siblings are probably the exception in this regard, so in those aspects I think your opinion generally represents the actual outcomes of homeschooling as it exists in the US, and probably is not that unpopular outside of homeschooling circles - but I would reiterate that I don’t think it’s intrinsic to homeschooling; rather, I think it’s a result of who in the US tends to choose to homeschool.
As for the idea that it stunts communal empathy, I’m a little bit baffled. I work in a mental hospital, one of my sisters has spent a year volunteering at orphanages in Ghana, one of my cousins (who was also homeschooled) runs a rural mission hospital in Bangladesh, etc… My observation is that most homeschooling families are rather pro-social and fully embrace the concepts of community and communal support of one another (even if they have eaten the socialism-is-bad propaganda; their rationale then is just that charity should come from the community itself rather than being subject to government mandate and bureaucratic inefficiency), so I’m curious what gives you that idea.