I don't think it's embarrassing unless you are concerned by labels and not the politics which underlie them.
We've seen in the last four decades that the Republican Party's doctrines are considerably changed. The party of Trump hardly resembles the party of Reagan.
Similarly, the Democratic party was fifty or sixty years back particularly focussed on accumulating votes in the south, as you observe, a fact which is now inverted.
The party of Lincoln, as I see it, bears little relationship to the modern Republican Party. I learnt this, if my recollections are correct, when reading the works of my favourite American, Mark Twain. I was at first baffled by his descriptions of the contemporary Republican Party, until I discovered the osmosis upon which you are commenting. The liberal (and not the woke) wing of the modern Democratic Party most resembles the party of Lincoln, in my opinion, but it is not an exact match. Whereas I cannot imagine the GOP fighting a war on behalf of black Americans today. Owning the libs is what Republicans want more than anything: it's the unifying slogan; also horribly empty of hope or constructive utility.
If you are interested, and I'm not sure you are, I count myself mostly an English Conservative, which is by no means the same thing as an American Conservative, and yet they fly under the same name. British conservatism is tethered to the ideas of Burke, who thought of his doctrines as pragmatic: whatever works is what is best. He was particularly enthusiastic about preserving institutions that have developed over time and wary of new ones unless they were necessary and served a useful purpose. He was very much not excited by the promotion of ideologies (capitalism! socialism!) and dogmas of the sort with which the American right (and indeed the British left) is so involved. Nor would he have had any interest in right wing labelling or left wing identity politics.
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