Mobile Suit Gundam: The Witch from Mercury was apparently based on a few elements from witch trials in the early modern period, but so far those bits of the series have been very forced/contrived. Apart from calling people involved with GUND-format tech “witches”, and a few trial/interrogation scenes, there isn’t really any theme of social hysteria or scapegoating going on.
Besides the “witch hunt” theme, a few Christian references like Cathedra (cathedral), Dominicus (Dominus/Lord), Michaelis (archangel Michael) have popped up. Again, these seem to be just theme-naming rather than actual fanatical anti-GUNDAM crusaders.
More interesting are the 2 recently-introduced Earthian Gundam pilots, Sophie and Norea. Since they appear together, it is probable that those names are a reference to Gnosticism: Sophia (wisdom) and Norea.
We’ll see if the writer/s do anything interesting with the Gnostic theme, but I’m not too hopeful on that point, as the plot twists have been very “Gundam-ish” so far.
As for Shakespeare references, his play The Tempest features Prospero, a sorcerer who lives in exile with his only child (a daughter), and commands a magical spirit named Ariel. That describes Prospera Mercury and Gundam Aerial quite well too, doesn’t it?