The fridges I am aware of have protection circuitry that shuts it down when the battery voltage goes below a certain voltage. That protects the battery from being totally discharged. The livewell pumps are a different story. To be fair to the manufacturers, the charges are really not intended to run full charge at a 100% duty cycle. With respect to my first point, a dual mode fridge (ac/dc) would be a better fit although a large expense.
Regardless, if the charger is putting out 30A, I would recommend replacing the fuse and holder with an ATX also known as MAXI fuse. These have heavier gauge leads and beefier fuse connections.
I do not know what the combined draw of the pump and fridge is but as long as it causes the charger to be a power supply as opposed to a charger. You would expect the fridge to cycle on and off and maybe be off more that on. So what is going on here? Is it just poor quality or incorrect fuse hardware?
Depending on the livewell size, pump capacity and species of bait stored in it, running the pump 100% of the time may not be optimal for bait life. There are timers that can be fitted that can be set to provide the correct aeration rate as well as reduce potential stress.
Here is a simple, fairly cheap example
Rig Rite, Livewell Timer, Automatic. Automatically turns livewell pump on and off.
www.go2marine.com