His/her vs their after using "each one" (for individual-focused meaning)

Solution 1:

Since all of your bullet points starts with a possessive pronoun, just move that up to the top line.

That means that you can use a longer phrase, because it's only used once.

Encountering a succession of people to observe how each one's way of thinking affects that individual's
● way of looking at the world
● ...
● ...

[I've made a couple of other small adjustments in the wording too.]