I can't find a table for this election, but for 2020, the most Republican state was Wyoming, with 27% (73k) still voting for Biden. Wyoming still got to ignore those 73k voters because the rule says the winner of the state takes it all.

Similarly in the other direction: aside from DC, the most Democratic state was Vermont, which ignored its 31% of voters choosing Trump.

Now consider that these are the most extreme states, and by definition, all other states ignored larger proportion of voters through winner-takes-all. Arizona had 49.36% D vs 49.06% R. Did the republican vote matter? Barely 10k more votes and the whole state decides all of its 11 votes are for Biden.

Yet somehow, no riots, no overthrowing state governments. (Yes yes we eventually had riots but that's a different issue - they were totally okay with the rules, they just didn't like the results.)

Popular vote is basically "Our state decided to choose what the majority of Americans want. The people have spoken, and chose candidate X. We're now honoring the decision." There's no reason why it should fall apart any more than the electoral college should.