Its is probably better in this case, though either would be understood and using one or the other would likely not even be noticed, particularly in spoken English. Since the antecedent of the pronoun, generation, is singular and nonhuman (though it does refer to a group of humans) using the singular, nonhuman pronoun sounds better, at least to my ear.
We commonly use it when talking about single groups of people acting together.
The noise from the crowd swelled as it grew from hundreds to thousands of people.
The team hasn't had a good season; it's lost a lot of its best players to injury.
If instead you had written:
The problem with the kids in this generation is ???? view of life.
Then their would be the correct choice, as it refers back to kids. Its would not be appropriate at all in this case, since the antecedent refers to humans explicitly.