What size fridge (and brand) do you have? Try to see if there is real world data on consumption that you can use to estimate your needs. Better still, try to measure its draw in the real world. I have a 52 L National Luna and some vehicle camp lights. I planned my bank assuming that on average I would be using 1.5A - 2A per hour or 36-48 Ah over a 24-hour timespan. My LiFePO4 is 50 Ah and I have 100 Watt of fixed and 60 watt of portable solar on hand.
Fridges do not run all the time. They cycle - a few minutes on to keep the temp and the compressor shuts down. The duty cycle will vary depending on a number of things - how you've packed it (empty fridge will cycle more often), ambient temperature, how often you open it, how well it is insulated, etc etc.
At the end of the day, if you are basically in need of a overnight camping setup where you are never stationary for more than 12 hours or so then you can probably just get away with a larger starter battery and a portable solar panel. A Group 27F is more than enough for that if you pair it with a 100 watt portable solar panel. You can carry a jump pack as an insurance. If, on the other hand, you want to camp a couple of days, then you are better off investing in a second battery with a DC-DC charger and some solar as a second source. With the cycle-life, and cost per cycle of a LiFePO4, I don't see any reason (unless its location, extreme cold/hot weather, etc) why one would want an AGM unless they want to install it in an engine bay setting.