GFCI tripping is likely a ground fault. Check welder grounding, my Hobart stopped tripping after I tightened it. Inspect cables for damage, And try a non-GFCI outlet for testing. Test with a multimeter, And clean connections with alcohol.
Welding near flammables is risky. Store chemicals in another room, my shop avoided fire. Use 3M P100 respirator, ventilate, clean spills with alchohol.