Late to the party here , so I'll ask questions to catch up.
Do you see a separate fuse in the distribution panel for furnace ?
The fridge and furnace are major 12 volt load systems and MOST RVs would have them on separate fuses and wires.
Can you disconnect and separate the two wires at the back of the fridge to see if both are powered ?
To confirm if the manufacturer used the stud at the rear of the fridge as a junction block .