The demands only seem inconsistent if you don't look at the actual principle underlying them. Political discourse tends to present opposing ideologies as being about principles like "free speech" or "free markets" - it's really all about power, who has it, and who wants it.
In this case its strengthening particular social and economic hierarchies - america vs the rest of the world, and white christians over non-whites or non-christian.
What's interesting is that this is not necessarily a struggle between the top of a hierarchy vs the bottom of one, but between two different hierarchies. The democrats support cultural non racial and economic hierarchies, while the republicans support racial international and the same economic hierarchies. So while they both support the rich over the working class, there is a struggle over whether to support racial and international hierarchies. Democrats tend to support globalization, i.e unifying of the power of the top of the economic hierarchy across international boundaries, while eliminating racial and sexual hierarchies as they are seen as "inefficient" from a neoliberal perspective. Republicans are more focused on the "national elite", the rich people that depend on america being a global hegemon specifically, energy industry, military industira-complex, etc..
Plenty of Democratic voters are on board with taxing the rich and flattening those economic hierarchies.
The problem has been that the Democratic party is the neoliberal wing of the establishment. Its purpose has been to create the illusion that economic progress is possible while working hard to maintain the economic status quo. Cultural diversity was the distraction and consolation prize.
Now the establishment wants full, unquestioned, totalitarian control now and no longer cares about maintaining the illusion of choice.
Ultimately it wants a country run on plantation lines with voting rights restricted to wealthy white male property owners, a "Christian" moral narrative (really just racism, greed, supremacism, and sexual opportunism dressed up in bible rags) and no independent sources of intellectual dissent.
Which means the bare minimum of public education, no science, no difficult or non-commercial art, no free thought in universities or academia, and as little free travel and contact with the outside world as possible.
The most comparable country is North Korea. So the likely end will be a heavily militarised and even more heavily propagandised country, run as a pampered inherited monarchy which tolerates a certain amount of education when it's useful, but is violently hostile to all dissent.
It's quite hard to get there from here. The shock-and-awe of the last few months were supposed to establish dominance, but it's not going to happen without resistance. Harvard is one example. There will be more.
Ultimately the military will be used to force compliance, and - absent a not entirely unexpected medical event - they'll decide which way this goes.