There really isn't anything weird or suspect about renormalization (except the name, perhaps). Read A. Zee's book on Quantum Field Theory.
This is the first time I've heard anyone say that. To me, renormalization is extremely weird, if anything because it's so unrigorous and ad-hoc that I find it hard to believe it even works. Sure, it does the job it's supposed to, and I understand how it does that (for the most part anyway), but that doesn't make it any less weird.
Like, ok, we get testable answers and they match experiments but also this is _so_ hacky and I can't shake the feeling that one day someone will come along and show that there's some reason why these bad assumptions work out fine. You know, like how "to find the Schwarzschild radius for a black hole of known mass, calculate the radius at which the escape velocity is equal to the speed of light" gives the correct answer even though the theory implied by this method is naive and wrong.
But doing splits and advanced acrobatics to get rid of infinities always felt like a hack (Feynman felt the same do at least I am not alone :))