Question about my homebrew

My Banes of Medusa are iron hands successors who (at first) realized the strength of the human temple, and due to a chaos warband band branch off, they are now divided by belief (kinda)

Basically I want them to be divided in three companies, 1 believing in the imperial truth, 2 believing in the God emperor, and 3 believing in the Machine God. Each led by the three "lore masters" who meet together to make decisions, and the unbiased chapter master who oversees the stability and general control of the chapter.

Basically im asking if this would be lore friendly at all. if yes or no, why or why not?