It can be. It can also have nothing to do with your preoccupation at all. Because the epitome of American virtue subsumes many things that have nothing to do with that "tension" or interpretations of Superman through the lens of an immigrant. There's entire books out there about it. In fact, here was a long-form Medium article from a year ago that delved into the philosophy of Superman following Zach Snyder's films. Ironically, in looking back at the Christopher Reeves films, and the socio-political trends of that decade in art, it mentions Superman as a foil to immigrant figures.
The wokeists may try to appropriate Superman as their own, but that's absurd, because he doesn't belong to them any more than the flag itself does. But it's most obnoxious here because they're clearly endeavoring to artificially manufacture a rejection of Superman by an American audience which has always adored Superman, and had no problem on partisan grounds with the anything they'd seen of this movie since they started hyping it last year.
Again, I feel like the article you site is engaged in the very tension and conversation I spoke about. Like I said, Superman is a popular tradition with countless collaborative creators. He's taken on all kinds of forms. But he's only "homegrown" through adoption. To argue against that is ludicrous. No version of the Superman mythos downplays his Kryptonian roots. And, as I've also noted, the question of what the adopted child owes to the adoptive family or what the immigrant owes to the nation that took him in, has always been central to the Superman story and the answer, as you point out, has almost always been a very much conservative leaning one of "a lot; the one who is taken in owes a lot to those who take them in."
As I said earlier, the film isn't woke. Like the Superman narrative as a whole, it just grapples with these issues. As I've also stated in one of my comments here, I think Ma and Pa Kent come off as the biggest heroes in this newest film, and they very much fit the archetypes of people who would very likely have voted for Trump. That's the entire point of addressing these large issues in the context of popular tradition: To bring nuance to the surface. The real world is complex. Likewise, Superman's world is complex.
You're also missing, or completely ignoring, the fact that the character was created by two young Jewish men, in 1938, as Hitler is starting WWII and rounding up Jews who are fleeing Europe and looking for places to take them in, in the absence of their own nation, which no longer exists. I mean, come on.
And for the record, even the Christopher Reeves films deal with this stuff in a deep way. The first film starts with him being put alone in a ship in an effort by his parents to rescue him from the coming death and destruction they are about to experience and give him a better life elsewhere. And then his adoptive parents strive to protect him by hiding his true origin, and teaching him to do the same. And then in Superman II fellow Kryptonians show up intending harm to his new home and he must decide whether he aligns with his birth home or his adoptive home, and even contemplates in that film whether he maybe should just fade into the background, and ultimately decides that he has a responsibility to his adoptive planet.
As I said before, and will reiterate, there's not very much that's "woke" in there, and as you suggest, the writing often leans more conservative and nationalistic (like much of DC's stuff traditionally has, especially in contrast with Marvel). But the story is pretty irrevocably wrapped up in the "stranger in a strange land" trope.