Should the power be off every time changing cables?

It really is a good idea. Better safe than sorry. I always do. Just not worth the risk. With speaker cables its easy to short out the contacts.

Don’t ever do that with RCA cables. It may be ok with XLR cables, but personally I wouldn’t risk it with those either.

RCA cables make the signal connection before the ground connection upon insertion, and break the ground connection before the signal connection upon removal. So when inserting or removing those connectors there will be a brief instant when the signal connection is present without a ground reference, other than the ground reference that may be provided via the AC safety ground wiring and whatever impedance in the components connects circuit ground to AC safety ground. Depending on the specific designs, the resulting sound can be highly unpleasant for both you and the equipment :-)

XLR connectors make the ground connection before the signal connections upon insertion, and break the signal connections before the ground connections upon removal. So it may be ok to do what you are proposing in that case.

Regards,
-- Al

Definitely turn them off.

The amplifier is definitely a component you want to keep off during any cable changes. It and the speakers are the most likely to have ballistic failures (as in, things fly) if you do something bad.
All other gear will be OK, with low voltages and low currents.

@almarg  and others...   To clarify, component off or system off?  If the component (for example Pre to Amp), then the Pre or the Amp or Both? Thanks.