So, it's worth noting that the GG (and the Guild in general) doesn't hate magic or magic-users. They have a bunch of both!
The issue is with people who are using forms of magic that they don't endorse.
Which, sure, appears to be controlling, but remember that one of those forms of magic is literally a death god whispering in peoples' ears and driving them insane. They're definitely controlling, but you can sort of see the reasonable foundation of their argument in there.
The story of the Guild is really one of corruption. Sure, you have the obvious corruption of the Guild Guard being the ones who are supposed to enforce the law but instead enforce a very biased version of it, but every branch has some corruption. The Public Relations Bureau is more or less there to push out lies and propaganda, and you can see how easily it corrupted Nellie from a champion of truth to a champion of truthiness. The Death Marshals, tasked with fighting against undead and necromancy, employ both of those things to do so, and the Neverborn Hunters are led by a woman with questionable parentage and a softness for Neverborn (she keeps one enslaved and has been seen riding one around from time to time).
The Witch Hunters are intended to keep a lid on unlawful magic, but most of that unlawful magic goes directly into Sonnia's personal libraries, a woman who uses forbidden magic to burn out peoples' souls and turn them into monsters. The Amalgamation Office was created to crack down on the process of Amalgamation, but its leader both kept an amalgamation on his staff and melded with machines in his avatar form. Lucius runs the judicial branch (and secretly, the Elite Division), both of which have been subverted for his own reasons.
Also, I like this thread! But let's try to avoid bringing up a bunch of real world political stuff, alright?