Identity politics aren't the problem-and it's not possible to be a "generic American"
We need to have some common points between people...but we can't actually create a single unitary "American culture".
What used to be considered a "common culture" was basically the bland, sanitized, Hollowood notion of what I'll call AngloEuropean Protestant "culture". It had almost no creativity, no vitality, no distinctiveness other than in the agreement to pretend there are no differences between any of us and that no culture other than AngloEuropean Protestantism should be treated with any respect, taken as a source of wisdom or insight or inspiration, or even allowed to survive.
And the "common culture" myth denies our basic cultural reality, which is that much, if not most of what we think of as "American" is defined by non-European elements(among just a few examples-I hope people add many more in response to this OP-virtually all forms of "American" music are based on African-, African-American, and Hispanic music, many American agricultural methods and many ways of surviving on the Westward path-a path that included genocide-were learned from the first peoples, American cooking is almost entirely defined by what non-AngloEuropeans brought to it)intersecting with and improving on what Anglo-Europeans brought with them.
We don't need to go back to the ugly days when everyone who wasn't AngloEuropean was forced to lose themselves, act like their cultures were shameful and must be cast off, and life was assumed to have basically stopped forever in 1953.
What we do need to do is to find the way to make sure that no one feels cast off and disregarded, that no one's hopes are forever ended, that no one is expected to just "take one for the team".
We need to find new ways to fight want, fear of want, and the fear of irrelevance...because it's the petri dish of those fears that breeds the culture of rage and backlash.
I don't claim to personally know how to do all that (I'm one guy posting on a website, not a damn prophet) but finding the way to do those things is much more likely to save us as a party and a people than giving in to the impulse to tell people to shut up, conform, and start losing themselves in the search for a generic republic that can never exist in any form other than fascism.