“After hearing that Ramin’s father was in the shah’s secret police who were responsible for killing millions…”
I thought the word would be “who” because police are people, but MS Word corrects is as “that”. I was wondering why “that” is the correct modifier?
When an entity (in this case a police force or police unit) can be viewed either as the sum of its human components or as an institutional and in some sense inhuman entity, the choice between who and that/which may serve to reflect the author’s preferred view. So if you see the police as humans collectively responsible for many deaths, feel free to overrule Word and use who:
After hearing that Ramin’s father was a member of the shah’s secret police, who were responsible for killing millions, …
On the other hand, if you want to emphasize the monolithic, institutional aspect of the shah’s secret police, you can treat “secret police” as a thing:
After hearing that Ramin’s father was a member of SAVAK, the shah’s secret police, which was responsible for killing millions, …
Either way, I wouldn’t use that in the construction you present, because (as far as I know) SAVAK was the shah’s only secret police organization—and if that’s the case, you don’t need to introduce a restrictive clause (signaled by that) to distinguish SAVAK from groupings of the shah’s secret police that weren’t responsible for killing millions.