All Level 1 and 2 EVSE have GFCI protection baked in to their contactor control. But they also have usually ground sensing technology and THAT separate circuit has the potential to trip an upstream GFCI, because it intentionally puts a test current on the ground to ensure a low resistance ground is available. If you google search it, there are some sketchy aftermarket EVSEs out there (probably no UL listed) that have ways to turn this off, if either the EVSE is ungrounded (they are NOT intended to be used this way), or if the circuit causes nuisance upstream GFCI trips.
This is rooted in UL 2231-1 & -2
(link to a 10 year old document). In a nutshell, a cord connected EVSE can have a 20mA GFI trigger threshold if it has a ground monitoring circuit, but the standard 5mA GFI trigger level remains if there is no provision for ground monitoring. The conflict is that this pre-dates the NFPA GFCI reqirements for EVSE outlets. IMNSHO, NFPA's gone off the rails with this and a number of other "modernizations", but that doesn't fix the issue, or the chasm between NFPA and the NRTLs.
In the real world, I first learned of ground monitoring when a friend tried to plug her Level 1 EVSE into my cord reel and it wouldn't work. The 30' reel had a 18/3 cord and grounded plug and connector, but internally these cheap reels have only two slip rings and connect the ground plug to the case, linking the cord ground via the central case screw. It's a tenuous ground connection at best (safe enough on my GFCI protected circuit), that wouldn't placate the EVSE's ground monitor. I switched to a nearby commercial cord reel that had three slip rings, and it worked fine.