Car stereo turns off when the cooling fan comes on

Car fans consume a lot of electricity, especially when first turning on.

Does your dashboard have a voltage gauge? If it did, you would probably see the voltage drop from 14v to less than 10v when the fans first turn on. After that the voltage would stabilize at 14v, or possibly a little bit lower.

This is why your cabin lights flicker when the fans first turn on. Lights will get dimmer as the voltage decreases, but your radio may be programmed to turn off when voltage drops below 12v.

If my diagnosis is correct, then you have nothing to worry about. It might be annoying, but it will not damage your car.

You can test this by purchasing a cheap multi-meter at a hardware or auto parts store. They typically cost under $15. With the dial set to voltage, hook the leads up the battery. It should read close to 14v when the car is running. When the fan turns on, like I said before, the voltage will briefly fall below 10v.

You could also check the connections to the radio because any corrosion/loseness in them would cause a voltage drop that is added to when the fan comes on.

Like someone mentioned, fans take a lot of current draw when they start. Normally your battery would be able to absorb the momentary high load, if it isn't happening you may want to test your battery.