The subject is the sort, which is singular, and singular subjects usually take singular verbs. Here we encounter the plural verb differ, which sounds correct because of the attraction of the nearby plural object justifications. It also seems correct semantically because it's the justifications that differ among themselves. To use the singular verb differs would require the sense that there be two or more sorts (or collections), something along the lines of
... the sort of justifications it does or does not get differs greatly from the other sort of justifications.
And there's no indication that the writer meant anything of the sort (so to speak). What the sentence means is
... the justifications of the sort differ greatly.
The problem with this wording is that there's no good place for the relative clause "[that] it does or does not get". So the writer went with the wording you quote. It is not unheard of, especially in British English, to have a singular collective noun take a plural verb if the members of the collective act separately. Thus you may encounter
Parliament have rejected the Corn Bill.
where Parliament is a single collective noun with a plural verb. Here, each member of Parliament presumably voted individually and separately his or her conscience on the matter.