I have a little different angle on this..
The reason that diodes were used between a panel and the battery is because when the panel is not producing power, it will have a parasitic draw on the order of 5% of its full sun current. Ie, during the day, the panel supplies current but at night it will drain current. If you put the diode between the panel and the battery, the diode isolates the panel at night and you eliminate the 5% parasitic draw.
However, about every solar charge controller on the planet also isolates the panel from the battery when the panel is not producing any current so you dont need a diode when a charge controller is used. You will NOT damage a panel by leaving a panel connected directly to a battery assuming the panel and battery are matched (ie, you have solar panel that is intended to be used with a 12 volt battery).
To the OP, you might ask the previous owner why he or she told you that. That would normally be bad info but maybe you have an additional problem with the wiring.
If you have a poor wiring setup, you could have some sort of problem. Normally you want the wires to the electric start (likely at least 6 gauge) to go directly to the battery. The wires from the solar charge controller also should go directly to the battery (more of less..)
Imagine a poor wiring case where the solar charge controller did not go directly to the battery but had a tap somewhere on the wires going to the outboard. When the outboard starter was being used, the voltage near the outboard could be lower than the battery voltage especially if the wires are too small. If the controller were tapped near the outboard, it would also see the voltage drop when the outboard was started. This normally will NOT blow the charge controller but it can send it off into the weeds as the voltage to the controller can get low enough for it to "lose its mind" but not low enough to cause it to reset once the voltage was back to normal.
With better wiring where the solar controller has a direct connection to the battery so you dont get something called ground bounce, you should be able to leave the controller connected to the battery while you start the outboard all you want. No need for any diodes. You should have fuses but the reason is to protect the wire from burning up in a short.
FYI, I have a charge controller connected to the battery and an electric start outboard. Charge controller is always connected to the battery when I start. Ive never had any issue doing this for years and lot of people also do this without any issue.
