First off, there is a distinction between restricting the use of slang in official settings and restricting it as a whole. The way it was explained in the update made it sound rather like the latter.
Second, given that we're not awake all of - or even most of - the time, you would think that people would be handling this stuff themselves. You know:
...providing facilities and structure for traditional cultural activities. Providing formal holidays within communities and specialized spaces, so that people can more easily practice and pass on their culture to the new generations.
We're not in charge of day-to-day life. You'd think that people would have instantiated these parts themselves. When people came onboard, they would have begun shaping the facilities to their needs, and establishing their schedules that fit their cultures. People would have figured out how to do the calendar and would have celebrated their holidays as before, because of course they would, it helps keep them sane and people like their culture! Christians will still celebrate Christmas, Chinese people will still have the lunar new year celebrations, Jewish people (assuming we have any, and it would be a shame if we didn't and lost what is maybe the oldest continuous culture) will still celebrate Rosh Hashana and Hanukkah and the like, because people don't just
stop doing that.
Do the traditions change over time? Yes, of course they do, and people try to preserve them, and this stuff happens
organically, no government intervention required. Hell, I'm fairly certain that almost every religion says that you should educate your children about the religion they were born into, so that they can do it properly.
Specialized spaces for this stuff? Of course people would have already carved them out of the available space. If nothing else, people will have made their own homes into spaces of worship, or at least made particular spaces within them for it. Hell,
any cultural practice will have this already; these people would have already had them, and they'll have made their new home to fit their culture just as much as their culture would adapt to space and their new home. This wouldn't even necessarily be obvious stuff - we're talking about stores, how housing is laid out, the presence of parks and where they are, so on and such forth.
I feel like you're overestimating how much culture changes over time. Does the paint job shift? Absolutely, go back 20 years and try to use our slang - or vice versa - and you'd be incomprehensible. But do the core ideas of culture, the core values, the core principles shift that much?
Look at a good 3500 years of Judaism and tell me.