For what it is worth my SquareD QO 20 amp dual function CAFI/GFCI (CAFI is Combination Arc Fault...) breakers to my outdoor outlets do not trip with my Lincoln 120V MIG, never, and I have many hours of welding with this set-up. In Canada arc and ground fault are both required on outdoor 120V outlets--why I have it. US may be different.
A few questions?
-How old is the AFCI, older ones had more nuisance trips?
-Have you tried a lower setting on the welder, maybe the breakers are tripping on current not arc?
-Is it a 15 amp breaker/circuit, related to above?
-Are the outlets back stabbed (bad) and what quality?
I did a bunch of research on this and had a thread on here about it as well.
https://www.garagejournal.com/forum/threads/afci-and-a-welder.335528/ Research wise overall
opinions were very mixed if it should be a problem or not but in general new CAFI breakers seemed to follow my experience (no trips due to arc).
On a regular 15 amp breaker I can trip it with my Lincoln (on current), why I am all 20 amp outside, 12 gauge of course, heavy duty outlets, no back stabbing..