I discovered this in the course of replacing an old ungrounded receptacle with a GFCI. I connected a run of lights controlled by three-way switches (two switches) to the load side. Afterwards, as soon as I flipped either switch, the GFCI would trip. It turns out that one of the lights in the run has its neutral routed back through the GFCI, but the other one is spliced to neutrals from other lights on the same circuit that are controlled by a different switch (diagram below). This gives two different routes back to the junction box upstream of the GFCI, which naturally makes it unhappy.
So first, is it ok to have a hot wire send part of its current back through a different neutral like this? If so, probably the simplest thing for me to do is just move the lights off the load side of the GFCI. If it's not ok, how should the wiring be changed?