If the two circuits are a true MWBC, fed from opposite bus phases, then the capacitance should be roughly equal from each of the two to the neutral. This minimizes the out-of-balance neutral current that will trip the GFCI.
But if one of the phases is always on, all the way to the end (receptacles) and the other is switched (lights), then whenever the lights are off the unblanced capacitive current may trip the 2-pole GFCI.
But in that case, I would expect the light circuit to also trip the GFCI IF the receptacle circuit is not energized.
What happens when you deenergize the receptacle circuit (downstream of the GFCI), turn the light(s) on, then if ithe GFCI holds energize the receptacle circuit? If the receptacle circuit then holds, one soution is to make the light circuit unswitched, with wireless remote switches at the far end instead.
Can you test by interchanging the conductors within the UF between the receptacle and light circuit? That (and probably the Megger test) will tell you whether there is some assymmetry between the two conductors in the UF.