Should the power be off every time changing cables?

You can make a lot of mistakes with an amp OFF, and it won't blow anything up. You make ONE mistake with an amp on, and it could be GOODBYE!  :) 

Miller’s suggestion about changing the preamp’s input selector switch while disconnecting RCA cables between the preamp and a source component will usually work ok, assuming that one remembers to do that.

But if the source component is solid state I would still not feel entirely comfortable about the possibility that depending on the specific designs a large transient could be briefly injected into the output of the source component during the instant the connection is broken, as I described earlier.

Also, if the preamp has a built-in phono stage it would be best to not set the input selector switch to phono mode when disconnecting RCA cables from a line-level source. If that were done it is possible that crosstalk of the brief transient I referred to could occur into the input of that phono stage, where it would then be greatly amplified by the phono stage, ultimately resulting in a significant thump in the speakers given that the preamp and power amp would still be powered up.

Regards,
-- Al

If muting is available does this mitigate risk?

I’m not arguing with the safer practice being to power down gear first but agree with the OP, it’s inconvenient, especially if tubes are involved.  

I’m guilty of doing IC and speaker cable changes while gear is powered up (though not speaker cables on a powered up tube amp).

My practice has been to switch preamp selector to an unused input (if changing an IC), turn volume to zero, and activate muting on both preamp and amp. Less risky?

My practice has been to switch preamp selector to an unused input (if changing an IC), turn volume to zero, and activate muting on both preamp and amp. Less risky?

Certainly! The only remaining risk that occurs to me is the one I described in the second paragraph of my preceding post, which IMO might in some circumstances create at least a slight risk of degrading the long-term reliability of the output stage of the source component.

Best regards,
-- Al

Thanks, Al.