Replaced and existing bathroom fanlight with a new fan/fluorescent light unit.
Existing circuit is on GFI breaker. Two switches provide power to unit. Shared neutral from switches to unit. After installing unit fan was fine. Light tripped GFI. Connected circuit to breaker and fan and light were fine. Reconnected GFI breaker. Removed fan unit from housing. While holding fan unit and light turned on the light and it was fine. Touched the fan unit to housing and breaker tripped. Reinstalled fan unit ; eliminated ground to light. The fan
And light work on GFI without the light grounded. (Tried another fan unit and light from different box/ same result.) Note: Unit has night light ; neutral was connect to other neutrals, power line was capped. Did not find any voltage on ground or neutral. Did notice that the lamp would flash when I plugged it in with the switches off.

Sure sounds as if there is a ground fault in the ballast of the light, or the ballast is not compatible with the GFI.

Is GFI protection necessary for this fan/light because it is in a shower or tub enclosure? If not, then a standard circuit is needed for this light.

Some ballasts have a normal fault current that GFI detects, and unfortunately not much can be done.