“That” refers to colonial and other boarding schools.

It's a relative clause rather than a 'that' clause and it defines which type of boarding schools we're talking about. You could replace 'that' with 'which'. [Schools in Xizang] are being compared with [colonial boarding schools of the United States, Canada and other countries that/which aimed to assimilate and persecute indigenous people] It's just a much more complicated version of a sentence like this: They compared [French apples] with [apples that/which were grown in Spain].

I pretty much agree with the others, however I think the sentence probably could have been contructed more clearly. I think THAT refers to the boarding schools, but it kind of seems like it could appy to the countries.

I’m just as confused as you are. I think it’s a terrible sentence.