AFCI breakers/protection and refrigerators - a bad idea?
The question presumes something I do not believe.

I don't believe all AFCIs also do GFCI at 30ma level.

This answer here is a very well-informed and interesting exposition on how many AFCIs were given a "weak" GFCI function to detect arc faults to ground.  But this was less than ideal - not least it requires you make a whole line of 2-pole AFCIs; in most of those applications, handle-tying two 1-pole AFCI would suffice if the AFCI didn't need to do that GFCI-ish thing. 

This lesser protection was typically 30ma.   Remember, 30ma protection is inadequate for kitchens, garages, basements or anywhere else NEC requires GFCIs. 

Some people believe AFCIs are required everywhere GFCIs are not.  The NEC does not say that.  If your local inspector says so, you need to have the discussion with them.  You can fight city hall, but it's cheaper to just replace that problematic fridge. 

Refrigerators are not the use-case for AFCI or GFCI

GFCI is to protect people from shocks, typically from lightly insulated plastic gadgets getting broken or wet, or the user having contact with an energized part of a 2-prong tool.  This is absolutely irrelevant to an immovable box with a steel chassis, all the 120VAC gear inaccessible at the bottom rear, and a fully plastic inner lining.  It would be nigh impossible for a consumer to contact anything 120V if they were trying. 

AFCI is to prevent fires from wiring faults either in house wiring or in plastic, flammable devices.  Being entirely contained inside an all-steel box, it's nigh impossible for a wiring fault inside the fridge to start a fire without also pulling enough current to trip the breaker.  Yes, the cord, receptacle or in-wall wiring could have a problem; but consider the same logic that is applied to the NEMA 10 receptacle: this is fixed equipment with a typically inaccessible receptacle, which is rarely unplugged or moved. 

Sometimes, a ground fault trip is a ground fault

I do see a lot of forum posts like 


  My old fridge never tripped the GFCI before.  Now suddenly it's tripping the GFCI a lot.  Why do fridges need GFCI protection anyway? Can I remove the GFCI protection?"  


Sometimes, a GFCI trip is exactly what it says on the tin --  "working as intended" genuine trip caused by faulty machinery.  Often cleared by a good cleaning, but sometimes, you just need a new fridge.  Insulation failure is one way machines fail.