Mains frequency changing all over the place? Why, are they running their generators with a guy on a bicycle or somtin? In any case, the mains frequency does not affect the tuner, the power is steped down, rectified and filtered as we all know.
All analogue FM radios have AFC, and it can be switched off on the good ones to allow tuning weak stations when they are near strong ones.
I remember H.H.Scott saying that AFC affects the sound quality, so it can be switched off on their receivers. H.H.Scott were famous for their FM tube tuners/receivers in the 50's and 60's.