Dtyjlui

So, in my world, there are a group of people, mostly unknown to the rest of the world, who took shelter from the apocalypse 90 years ago in great underground bunkers.

Compared to the rest of the Wasteland, they live in a utopia (except for all the xenophobia, fascism, and euthanasia). They have access to clean water, plentiful food, and so on. Basically, they live a modern style of life, while the rest of the world has returned to early 19th century.

So, my question is, considering their lifestyle, would the Bunker Dwellers have any noticeable genetic differences to Wastelanders, after 3-4 generations underground?

Genetic no.....

Physical yes. Ample food, modern healthcare and clean water means they would be healthier, taller and good teeth. Skin would be paler and less blemishes.

A child's access to health and nutrition greatly impacts on height, strength and intelligence later in life.

Genetic changes are only really likely if the vault dwellers use genetic engineering to improve themselves or wasteland dwellers suffer from radiation caused diseases.

3-4 generations are not enough to establish noticeable differences between populations.

The only noticeable differences will come from the different diets: those with a richer diet will grow better (taller, bigger), while the other will necessarily reflect the much poorer diet.

For a visual reference, you can look at the famous Robert Capa's photo of a Sicilian farmer and an American soldier during WWII:

You can clearly perceive the difference in size between the well fed American soldier and the farmer. Something similar would be present in your case between the two groups.

But it won't be based on genetic differences.

There are likely to be genetic differences, but ones that were present at the time the groups split.

Who had access to the bunkers? I'm sure it was not random luck.

The other differences will be that people with a variety of disabilities and health conditions (which may or may not be genetic) are more likely to die off if they are in the wasteland. Since most such conditions are genetic only in terms of how likely you are to get the condition, this will probably not affect the actual genetics. Yet.

For example, there aren't going to be a lot of wastelanders with conditions that affect their stamina (running away from danger), eyesight, or mobility, for example, a heart condition that shows up under physical stress. But the genetics involve multiple alleles throughout the genome (not a single inherited SNP) so it is way too early for this "natural selection" to change the gene pool in any significant way.

Though even one generation can change epigenetics. Methylation markers on the DNA itself that turns certain alleles on or off. Epigenetics can carry information acquired after birth and pass it along to the next (unborn) generation. It does not change the actual DNA but markers are inherited to a degree. Something like famine can affect generations that never experienced it.

None. None at all.

90 years? Unless life in the wastelands is unbelievably hard, you have a better-than-average chance of someone still being alive in the wasteland who was there (even if they couldn't remember) when the bunker was closed.

How much genetic difference do you have with your grandfather? Or, at very worst, your great grandfather?

None, of course.

@L.Dutch is right, the environment could bring some differences, but even that wouldn't be horrible. Give the wastelanders a bath, dress them in Fallout Bunker clothes and other than their tan and possibly and accent, you wouldn't be able to tell the difference between them.