So, I assume that if you put 100 people on a spaceship and sent them to wherever, they’d get very inbred in a few generations. How many people would you need for this to not happen, accounting for the fact that there will eventually be people who are infertile or die before having children?
Around 4000.
As I understand the article, it relates to the wild conditions. There is some evidence of lucky population that can survive after only 20 human bottleneck - https://en.wikipedia.org/wiki/Pingelap. And humanity itself could have faced around 1000 spices bottleneck - https://en.wikipedia.org/wiki/Population_bottleneck.
That does not apply to humans who are capable of intentionally avoiding certain breeding problems, and also who have medical knowledge that can apply even if it does happen.