Technically, you can stop evolution from happening. Cloning is annoying, but if you had enough compute and algorithms you should be able to make in-place edits to stop drift. By "in-place" I mean even optimistically just a bit after the blastocyst phase, editing humans that are even slightly grown to that level is just not going to be practical.
> Technically, you can stop evolution from happening.
Yeah, but would anyone do that to an entire civilization? Evolution leads to greater 'fitness' - improved adaptation to the environment. The travellers are jumping from $HOME_PLANET, into a generation ship, onto a new planet presenting novel adaptation challenges. That planet's star-system then eventually sets off on a long journey, until it encounters a new star. Each of these stages takes many times the time humans have existed on Earth. If you consider only modern humans, we've only been around for 50,000 years, maybe.
And "modern humans" isn't a civilization; it's really all of the different, successive human civilizations.
If you could imagine that, in addition to making stone tools and animal-hide clothes, neanderthals had also learned how to freeze evolution, do you think those guys would be well-adapted to a planet-hopping future? I don't.
Once you have the technology to freeze evolution, you also have the technology to accelerate it and steer it, and given the level of incentive (to gain competitive advantage), I don't imagine it would be a balanced sword-and-shield race in the long run. The "conservatives" couldn't keep up with the "modernists", unless it's some sort of a totalitarian system.
There's been this great (relatively) short story, both humorous and profound, by Stanisław Lem; "The Twenty-first Voyage" in "The Star Diaries". It's based on that exact premise.
