Disturbing a transformer's field

How sensitive are (let’s say toroidal) transformers for external disturbances affecting the precise uniformity of their field?
Does it matter so much what’s happening at the fringes of the effective field, seeing that the intended function of a transformer is happening in its very near proximity?
If I lined the casing of my amplifier with mu-metal, could it be detrimental to the performance of the dual 650VA transformers? How much do these things need to “breathe”?

(In my situation they’re “breathing” enough to induce audible mains hum to the output through induction via the phono preamp’s ground wire. Made me realize that even phono ground wire should be well shielded)

I believe they are impacted (some would say audibly and therefore not stack components), worse in some directions than others (less so on the “horizontal” plane of the torroid).

Yes, you have to be careful with mu metal. It can cause electro magnetic fields make their way somewhere they shouldn’t be and therefore harm sound quality or maybe even parts although they might help avoiding hum you might have had as a goal.

Not sure if it disturbs the transformer, but as I said, it might direct the transformers field elsewhere to an unwanted place.

My experience is, mu metal (if you don’t know exactly what you’re doing with limited specific measures) should only be used outside of components and between two components.