Several European countries have established churches, and in some of them that established church does have a special role in lobbying, or it gets a seat in parliament, etc. That hasn’t stopped those countries from being regarded as well-functioning democracies. So, a knee-jerk reaction that this is a direct road to theocracy and dictatorship is a bit much.

What is problematic in the US context is that the majority of the population doesn’t so neatly subscribe to a single faith, not even historically. The US has always been a mix of, first, the “mainline” Christian denominations, then since the early 19th century a mess of neo-Protestant sects, and finally every world religion. So, I think would have to underscore that it is this particular environment that trying to establish any religion as advantaged would require some authoritarian steps.