Inductive kick from switching a starter motor off does not get
transmitted to the electronics. The inductive kick comes from the
induction of the windings in the starter motor when the current is
interrupted. But if the current has been interrupted it is no longer
connected to the battery so the spike is restricted to the starter
motor side of the switch.

Radios and accessories in a vehicle are turned off during cranking to
minimize additional loads on a struggling battery so its full output is
available for the starter motor. It has nothing to do with protecting
the electronics.

The problem with low voltage drop-out is when you have computer based
equipment that takes forever to re-boot or radar which has to go
through a warm-up delay before applying power to the magnetron.
Turning these off to crank an engine and then having to wait for them
to re-boot is not only frustrating but could be dangerous if you had an
engine failure in an emergency situation, right when you may need that
radar or depthfinder the most.

Most modern marine electronics can accept a very wide range of input
voltage so it sounds like the voltage is dropping too low during
cranking. As suggested above this could be a bad battery connection
(check the GROUND connections too) or it could be a battery failure in
progress.

If you have a combiner and a house battery, move the sensitive
electronics to the house battery where they will not be subjected to
the low voltage during cranking.