Norcold fridge and furnace fuses keep blowing.

Is the fuse you are replacing a 30 amp or 15amp?

It appears that fridge AND Furnace are supplied DC form SAME FUSE.....

Fridge disconnected...fuse still blows so that eliminates fridge
Thermostat disconnected...fuse still blows so that eliminates the thermstat but NOT the furnace

SO....
Need to disconnect 12VDC at furnace....should be RED wire and see if a new fuse still blows
If it does.short in DC wire to furnace
If it doesn't...short in furnace (could be relay, circuit board, switch etc)

Brand/Model of furnace??????

With gen on, the converter would be on making "12v" and running the 12v things and charging the battery if it needs charging.

Converters can go bad and go over their usual voltage outputs of say 14.4v in boost. The fridge has a DC limit of 15.4v. Perhaps the converter has pushed the 12v system voltage above the fuse limits.

You need a voltmeter to check things out. Meanwhile kill the converter's 120v circuit breaker while the gen is on. You should still get 12v (the proper values) from the battery before it runs down. Meanwhile you can find the problem. You can use a regular portable battery charger if the battery does run down.