I don't think there are any firm agreed on measures of language similarity, so in that sense the question is unanswerable. But here's an attempt to use the term-usage-frequency data in google ngrams to partially answer your question.
First question, is the cultural revolution visible at all in the google ngram corpus? There are some obviously revolutionary terms like 阶级 or 斗 that you'd expect to spike in the 60's-70's range if the corpus has any sane connection with current events.
https://books.google.com/ngrams/graph?content=%E9%98%B6%E7%BA%A7&year_start=1800&year_end=2000&corpus=23&smoothing=3&share=&direct_url=t1%3B%2C%E9%98%B6%E7%BA%A7%3B%2Cc0
https://books.google.com/ngrams/graph?content=%E6%96%97&year_start=1800&year_end=2000&corpus=23&smoothing=3&share=&direct_url=t1%3B%2C%E6%96%97%3B%2Cc0
Ok so that test passes. For this particular measure of language change, rather than trying to find cultural-revolution neologisms, a better yardstick might be to look at the most common words
Here's the popularity of 之, which I'd expect to be associated with high-register 'fancy' Chinese:
https://books.google.com/ngrams/graph?content=%E4%B9%8B&year_start=1800&year_end=2000&corpus=23&smoothing=3&share=&direct_url=t1%3B%2C%E4%B9%8B%3B%2Cc0
It crashes when baihua takes over and flatlines after that. So the cultural revolution didn't have much impact on that particular change that was already going on.
I had hours of fun trying this with a bunch of different words, but I think 警惕 is a nice representative example.
https://books.google.com/ngrams/graph?content=%E8%AD%A6%E6%83%95&year_start=1800&year_end=2000&corpus=23&smoothing=3&share=&direct_url=t1%3B%2C%E8%AD%A6%E6%83%95%3B%2Cc0
It explodes into the corpus around the baihua-takeover time when 之 first crashes, then spikes for the cultural revolution when being 警惕 to all sorts of things was very important, then basically drops back to 1950's levels in the '80s. To get a proper answer you'd need a much more systematic review than I have time for, but my impression is that this pattern is pretty typical.
One interesting case is earthy dongbei-style terms like 到底 and 啥. These are things I'd associate most strongly with distinctively 'mainland' usage, and they're also "peasant's own" terms that definitely did spike during the cultural revolution when everyone was competing to be more 老百姓 than their 99 neighbors. But check out the trajectory of 到底.
https://books.google.com/ngrams/graph?content=%E5%88%B0%E5%BA%95&year_start=1800&year_end=2000&corpus=23&smoothing=3&share=&direct_url=t1%3B%2C%E5%88%B0%E5%BA%95%3B%2Cc0
I think just like 警惕 it's reasonable to draw a straight line between the 50's the 80's, only this one is a sloping line rather than a flat one. Although these earthy terms were definitely sensitive to the politics of the cultural revolution, their rise pre-dates it and continues after it.
It's a shame ngrams doesn't have a 繁体 corpus, the comparison would be really interesting and give a much better answer to your question. But I think the ngram-scraping perspective suggests the answer to "how much did the cultural revolution change the Chinese language on the mainland" is that language changed dramatically during the revolution itself, but basically returned to 50's baselines by the 80's, although there are other (quite possibly mainland specific) language-change trends going on over that time, like the rise and rise of dongbei influence.