Society should not be based on any ideology or academic theory, but some of them will always be part of the environmental pressures that influences society. That's how part of how societies work, that's how academia often tries to work.
Not everything that you've listed comes from critical race theory or even academia. Person of color originated in the US as an identifier by European colonists centuries ago, then became a term of political solidarity. It was used for decades this way before it became academic or mainstream. Woke originates from AAVE and music lyrics, I don't think I've actually seen it used in academia outside of some catchy article titles.
Yes, CRT originates in US Black Liberation concepts decades ago. The universal application of it has many issues. The use of the word privilege has many issues that have been up for debate for decades. The only place where it's all held as all fact or all fake & simple seems to be media & internet discussions. CRT is a complex theoretical framework with many differing opinions within those who agree with most of it and those who don't, just like many others. We're never going to get a perfect one and any attempt at a unified social theory will have major problems.
Christianity has not and never has been a unified force in society. From the texts (whole speech by Jesus about bringing the sword and dividing families, a lot of the text is about dividing people) to the early churches rewriting some of the texts to fit their choices for canons, to other texts being destroyed in the name of keeping that canon and dividing others off as hell-bound heretics all the way to today where we have dozens upon dozens of denominations many of which have major issues with nepotism and other types of dividing corruption & some active hatred towards each other. Christanity is as much of a dividing ideology as CRT, it just has more people using it to explain society and as a carrot & stick to (dis)incentivize behaviours.
Ayn Rand's survival and personal happiness as the ultimate values, and that altrusim is a scourge on morality, is also a dividing ideology. Her works create a clear tribal divide between those who make it in a capitalist society and those who don't who she literally discussed as leeches. She was, and the Ayn Rand Foundation is now, really big that society and the law has no right to punish racists, homophobic people, or anyone else. That there is no ethical point in being against others choosing to hate others.
Yes, we will be judged by later generations just as those generations alive now judge each other. We tend to judge them by the legal and ethical (socially incentivised morality) because often that's what we evidence for. It would be good if more historical discussions could discuss personal morality through time, but it's a far more difficult topic to cover. People's personal moralities, debatably, should be higher than socially acceptable ethical minimums and the legal baseline is not a basis for morality at all. Personally, I hate the whole 'wrong side of history' argument because we're not and never can be in control of that, but it's not an argument for not analysing the legal and ethical failures of our ancestors. One of the best ways to prevent ideological thinking is to analyse and show that no 'hero' is perfect, to look at policies and their effects, not individual people or theories.