Your example sentence -
Another implicit process that probably affects women is the tendency for people to select those whom they will feel comfortable working with.
for people act as the subject of the infinitive clause - to select those whom they will feel comfortable working with.
Now if we omit for people, how does it affect the sentence?
In that case the sentence will look like the following -
Another implicit process that probably affects women is the tendency to select those whom they will feel comfortable working with.
This sentence means that it's the tendency of the women to select those who they (women) feel comfortable working with. And the implicit process that affects the women is this tendency..
But your original sentence means something completely different -
Another implicit process that probably affects women is the tendency for people to select those whom they will feel comfortable working with.
Here it's the tendency of the people, not that of the women. And that they refers to the people, not the women.
You can't play around with the position of the subject of the infinitive clause. It's a fixed position - for A to verb ....
For further study about this, please go through this link.