As I said, any category of culture will have changed in so many ways from 1960 to 2020 that it is far from unreasonable to say that the changes are immense. Anyone living today with pretty much 100% certainty is not practising 1960s culture, people have adapted with the times, it is not a matter of me going out and meeting older people.
Remember that we're talking about culture, businesses lasting hundreds of years is not relevant to the culture because that business will have adapted with the times. Of course, today's technology is built upon the technology of yesterday, but if I said that technology in 2020 has advanced a lot since 1960, that'd be true regardless of this last point and so it is.
We can categorise the changes from 1960 to 2020 in two ways, firstly, the ways things which existed in 1960 have changed and the effect of new things which came into being between 1960 and 2020. As for the former, nothing is unchanged, for instance, you acknowledge the changes for women and homosexuals have been significant but let's look at heterosexual men. I will just list some things.
Meeting your partner
https://flowingdata.com/2019/03/15/shifts-in-how-couples-meet-online-takes-the-top-spot/
https://news.stanford.edu/2019/08/21/online-dating-popular-way-u-s-couples-meet/
Getting Married
https://www.thespruce.com/estimated-median-age-marriage-2303878
Going to college
https://en.wikipedia.org/wiki/Educational_attainment_in_the_United_States
Fatherhood
https://www.nytimes.com/2017/08/30/health/fathers-united-states-age.html
Number of Children
https://www.statista.com/statistics/718084/average-number-of-own-children-per-family/#:~:text=The%20typical%20American%20picture%20of,18%20per%20family%20in%201960.
The decline of Nuclear Families
https://www.ozy.com/news-and-politics/the-nuclear-family-is-in-decline-but-did-it-ever-represent-america/258493/
Increase in Single Parenthood
https://www.pewsocialtrends.org/2018/04/25/the-changing-profile-of-unmarried-parents/
We can look at changes in divorce, hookup culture, homeownership and types of homes, the effect of females joining the workforce, stay-at-home dads and like I said, pretty much everything will have either changed a bit or a lot.
That's the group you said didn't have big changes but is that really true? I automatically assumed you meant white heterosexual males because I doubt you'd argue that 1960s and 2020 is similar for the majority of ethnic minorities in the US. Every other group has clearly gone through far more changes than this group which has clearly changed a lot.
It's not a question of whether this one thing convinces you, it's just that I could do this for genuinely any cultural thing you want to talk about.
Then there's the stuff is really different, the explosion of computer, phone and internet usage from the 1960s to 2020 has revolutionized businesses, entertainment, education, sex, income, social interaction and the list goes on.
English has clearly changed a great deal, it's not that words are being changed but rather becoming more or less common. How could you even attempt to say that 20-30-year-olds today are speaking as they did in the 1960s? It's not even possible for them to do when the things they're referring to often didn't exist in the 1960s. Whether it's the internet, film, television, education, so much which has had a profound cultural effect in the last sixty years, why would it be barely changed?
As I said, any topic you want to bring up, I can do this, because you are severely understating the differences. If you want to agree to disagree that's fine but do not misrepresent my position, I'm not saying I can't understand people from the 1960s, I'm saying the culture has changed dramatically. Be careful about what you say is not a significant change because at some point, you will effectively end up denying there's any difference between any of the Western countries because the differences are there ar less substantial than many of these ones.