Thought experiment, if a bunch of people went to live underground, would they evolve differently? Assuming they would live, die and reproduce the same as they did on the surface?
Like, does evolution only stem from survival of the fittest, or does our offsprings genetics change at all from the environment (outside of radiation and such of course)?


Death is not the only driver. Reproduction is by far more important. Death only affects evolution because it prevents reproduction. With modern medicine then sexual selection becomes a bigger driver.
And even then evolution will always happen as mutations will always happen. Even if it is mostly just random drift in features.
We see many aspects of this over and over. Birds on island tend to lose their ability to fly. Larger animals on islands tend to shrink over time. Even isolated humans in extreme places (like high up on a mountain or that do a lot of deep sea diving) show adaptations to their environment. Once isolated even small pressures on your ability to reproduce will affect the population over time. It just might take a lot longer.