I was surprised to find that after replacing most of the op-amps in a ADA MP-1 pre-amp, most of that orientation-sensitive remaining buzz that you still get with humbucking pickups was seriously reduced.

When I'm playing at a low volume, I can just mute the strings and put the guitar on a stand to get it to be quiet. On a high-gain program using the tube board and all.

The reason for some of the buzz is that the circuits are amplifying common mode. The op-amps are operated in feedback meaning that the - and + inputs are at nearly the same voltage. However, the incoming common mode noise moves that entire voltage; and it's possible for the common movement of +/- to itself be amplified.

So that is to say, suppose you have this representative single-ended stage:

                     |\
  in --)|---+------- |+\
            |        |  > ---+---  out
            <     ,- |-/     |
            >     |  |/|     |
            |     |    GND   |
           GND    `----------'
             

The guitar cable's shield is connected to GND. Now suppose that GND is oscillating at 60 Hz due to the cable shield picking up EMI. (The cable shield is a big area of copper bathed in noisy electric fields, with nothing shielding it, and is galvanically connected to your amp!)

This means that the (+) node of the OP amp is seeing this fluctutation, and due to the feedback the (-) node is following.

An ideal op-amp will not amplify any voltage offset that equally affects (+) and (-). But real op-amps do. The degree to which they do not is the CMRR (common mode rejection ratio) which is a data sheet parameter that is better in some parts than others.