There is certainly a history in the US of voting suppression targeted at racial minorities, especially African-Americans. (And although I am indeed not an American, my own country also has a history of racial discrimination in voting, also within living memory–the US is less unique in that regard that you seem to think it is.)
However, if working class non-Hispanic whites appear to have been switching, over the last several elections, from Democrats to Republicans – it isn't clear how voter suppression explains that particular change. Your theory suggests that working class non-Hispanic whites haven't changed their collective political allegiance at all, it is simply that Republicans have managed to selectively suppress their vote, but only of those among them who vote Democrat. I don't think that's very plausible – it isn't consistent with the observed changes in turnout figures. And a history of electoral discrimination against racial minorities isn't very relevant to that theory either, since to explain this it would require, not voter suppression against a racial minority, but rather large-scale politically-selective voter suppression against the historical ethnic/racial majority, which is a rather different thing.
And, it isn't just non-Hispanic whites. The biggest swing towards Trump between 2016 and 2020 was in Laredo, Texas–27.7 percentage points. [0] And Laredo is over 95% Hispanic, indeed the most Hispanic city in the United States outside of Puerto Rico. It is also not a rich city by any measure – 30% of its population are below the poverty line. So, it looks like a significant chunk of Hispanic people in Laredo (and elsewhere in southern Texas) – many of whom would be of lower socioeconomic status – decided to switch their vote to Republican, or turnout for the first time for the GOP, in 2020. And the idea that, instead, Republicans just worked out how to suppress Democrats from voting, is inconsistent with the fact that turnout actually increased in Webb County from 2016 to 2020. [1]
[0] https://www.nytimes.com/2020/12/07/upshot/trump-election-vot...
[1] https://www.sos.state.tx.us/elections/historical/webb.shtml