From what you've said either the fridge or the battery charger is faulty.
I disagree, OP says it still trips when both are switched off.
However it still trips out the electrics even when these are both turned off.
Which, to my mind, indicates that the problem is between (and inclusive of) and the breaker and the on/off switch on a device.
i.e. the breaker,
the cable from the PDU to the battery charger socket / the battery charger socket / the battery charger plug/ the cable from the battery charger socket to the battery charger / internal wring in the charger
as above for the fridge.
For me the first step in problem solving is to apply Kepnerr Trego logic and ask your self "As anything changed since there was no problem"
If so concentrate on this.
Next step is to ask yourself "Are there any easy cheap meaningful checks I can do, to eliminate probable causes?"
In your case, swap the breaker, because this is most likely cause of the problem; is relatively easy to and involves no expense.
Now it is a case of divide and conquer! (To give it the posh name this is "binary chop" trouble shooting, you keep reducing the possibilities and eventually identify the fault).
The easiest way to divide your problem is to decide if the problem is before of after the device plugs.
Un plug both devices from their sockets and see if things still trip.
Continue dividing the possibilities.
Good Luck