Malcolmite and anti-Malcolmite
Both Malcolmite and anti-Malcolmite are nouns. One refers to followers and supporters of Sir John Malcolm, a British envoy in Persia in the late 1820s, and the other to opponents of Malcolm. "The Malcolmite MacDonald" is Malcolm's brother-in-law, John MacDonald, who, not surprisingly, is a supporter of Malcolm. Edward Ingram, on the other hand, is said to be a modern-day anti-Malcolmite; according to the quoted text, he wrote an "extremely biased book" that was highly critical of Malcolm—but he did so in 1984, more than 150 years after the historical events that Malcolm was involved in (Malcolm died in 1833).
All of the background information I have just provided comes from the article that the poster cited: Firuza Melville, "Alexander Sergeevich Griboedov: Russian Imperial James Bond Malgré lui. In Memory of the 225th Anniversary of His Birth," in Rudi Matthee & Elena Andreeva, Russians in Iran: Diplomacy and Power in the Qajar Era and Beyond (2018). You can read seven of the first ten pages of this article in the linked version of the book.
With regard to the English suffix -ite as used in the terms Malcolmite and anti-Malcolmite, Michael Quinion, Ologies and Isms: Word Beginnings and Endings (2002) offers this relevant entry:
-ite Forming nouns. {French -ite, via Latin -ita from Greek -ītes.} Some examples are the names of an inhabitant of a place or country: Canaanite, Israelite, Muscovite, Seattleite. Others refer to a follower of a movement or doctrine, especially one marked by -ISM: Hitlerite, Jacobite, Labourite, Luddite, Thatcherite, Pre-Raphaelite, Shiite, Trotskyite.
Quinion goes on to discuss other uses of the -ite suffix in English, but for present purposes the "follower" sense of -ite is the relevant one. Evidently, Firuza Melville thinks that Malcolmism and anti-Malcolmism constitute sufficiently coherent political or sociopolitical orientations to have attracted adherents—Malcolmites and anti-Malcolmites.
With regard to the phrase "the Malcolmite MacDonald," the words "the Malcolmite" are certainly being used to characterize MacDonald, but this construction is not syntactically different from referring to him as, say, "the diplomat MacDonald": like diplomat, Malcolmite is essentially a noun being put to work in apposition to another noun. Still, it is true that Malcolmite could be used as a pure adjective, as in the phrase "Malcolmite sympathies"; there, the sympathies are not themselves Malcolmites, so the term Malcolmite is functioning entirely as an adjective modifying sympathies, to indicate what kind they are.