Unless the voltage is reduced using a switching type regulator, regulating down to 12 volts will throw away 50% of the power you are taking out of the battery in the form of heat. Really bad on your energy budget. This is not speculation.
The down-side of the switching type regulator is the difficulty of elimination RF radio noise caused by the internal square wave. It can be filtered out, but no surprise if you got all kinds of electrical interference from it. It really makes more sense to not regulate down.
Ken
1. Switching regs are dime a dozen anymore, and halfway decent filtering will take care of the RF noise. The one I've got on my autopilot project cost like $3 and has no noise at all. Was easier to just use a cheap premade reg board than design one. (ok, ok, I lie. I can see some noise on a scope, but there's a pretty good inductance with the lengthy wire to it, + some filter caps, + the fact it's not powering much but an arduino so it's 100mA or so.. no noise affects anything in the boat including VHFs and AIS. )
2. Just the fan - not the compressor. The compressor already handles 12 or 24v anyway - so the fan is the problem. Likely pretty low power at 12v - or you wouldn't use it on a boat anyway. So even a linear reg wouldn't be the end of the world - 'cause it'd be blowin power when shore power was connected, so who cares about power waste in that case.
Now that I think of it, if the compressor will run at 12 or 24, why won't the fan? I.e they sell that "rectifier" (which I'm reading as British for "Power Supply") to run this very fridge. So if the comp is dual voltage, why isn't the fan? I assume the control board is regulating power somewhere to both the comp and the fan. Hmmm... I may need to investigate it for my own curiosity. If there's a relay - always power from 12v would work fine here.