2 GFCIs out of one box to different circuits
"mysterious grounding" may be the problem. A GFCI is very sensitive to grounding problems - by design. A few questions:

1 - Do the GFCIs trip and not reset? Or do they NOT trip but simply "don't work"? There is a big difference. If they trip and won't reset then there is a real grounding problem. If they don't trip then they may be bad, though unusual to have two brand new bad outlets.

2 - I'm a little confused about the circuits. "feed separate circuits" implies 2. "They worked before supplying one circuit" implies 1. Do you have 2 separate circuits - i.e., two separate circuit breakers in the panel? Or do you have 1 circuit that originally supplied the openers and now also supplies an outlet? If you only have one circuit then you should only have one GFCI installed.

In addition to any other "mysterious ground", it is possible you have a problem with the openers - i.e., a fault that is minor enough to not trip the regular circuit breaker but is enough to trip the GFCI.

I don't know whether an opener circuit by itself (i.e., no outlets on the same circuit) needs GFCI protection according to code or not. Harper or ThreePhaseEel or one of the other code experts can answer that.