Dropping the 4E aberrant origin and Far Realm lore was a missed opportunity!
In the context of removing noninclusive texts in 5e, perhaps removing racist supremacist Lovecraft material finds a new opportunity to drop Far Realms.
As far as I know, "aberrant" is a D&D term (not a Lovecraft one?).
If so, using "aberrant" to mean grotesque mutant, seems ok? The difference between "monstrosity" and "aberrant" seems to involve intelligence, similar to the difference between "beast" and "humanoid".
Hm, how would we implement that as an option without making it frustrating for the players or the DM?
To actualize reality warping tropes.
At low tier, maybe mechanics of: difficult terrain, descriptions of sites and objects that are askew, a devils bargain that grant abilities but mutates a character to grant it, creations of cursed items, etcetera. Maybe exhaustion attack represents a temporary mutation, but a corpse at zero hit points fully mutates, while a Remove Curse can restore to original wholesome health.
At mid tiers, "summoned" creatures are actually locations warping, becoming new aberrants. Even if dead, their mutations remain. But Remove Curse can restore these kinds of aftermath.
At high tier, legendary actions can be the warping environment making attacks autonomously.
Something like that. Mostly normal mechanics can actualize the trope.
I feel a "curse" that can be cured, helps convey that the dehumanization is Evil (Neutral Evil), and that humanity can prevail when removing the curse.
But there can still be edgy characters, who choose to mutate to gain certain abilities. Player characters can be Good aberrants, who undergo the loss of humanity for altruistic motives. This resembles a Warlock Devil Pact, where it is possible to be a Good Warlock, if the player chooses this concept.