Although it's a requirement, the mobile charger has its own GFCI
It does. But that can only protect farther down the line, at the plug end that goes into the car. If you are standing in a puddle of water and are attempting to plug it into the wall, and your finger slips and touches the prongs, there's a shock risk there that GFCI in the circuit could help, but the GFCI in the charging cable wouldn't be involved with. That's just why the NEC has that requirement.
and they're said to cause trips between each other.
Unfortunately, yes. But it's not so much because of having two GFCIs on the same circuit. It's because of a ground test that the charging cable does. It trickles a tiny bit of current onto the ground pin to see if it seems to be floating (bad) or is tied hard to ground at 0V (good). Unfortunately, that is exactly the kind of condition that GFCI is looking for and attempting to prevent, where current is not exactly matched on the two voltage pins. The current used for that ground test is very tiny, and is supposed to be below the threshold that the GFCI would trip at, but that threshold level is also very tiny and close to that testing amount. So if the GFCI breaker is a little out of spec, it can have nuisance trips from that ground test.
It's kind of a pain, but that's what the code requirement is, and is yet another reason why the wall connector is getting to be a better choice, because those hardwired ones don't need to have that touchy and expensive GFCI breaker.
Is there a recommended solution for this?
The solution isn't great. If the GFCI breaker is a bit out of spec and doing this initially, or drifts out of spec in a few years and starts doing it, you need to replace it with a newer one that hopefully is in spec and stops doing that.
Does the GFCI requirement render all mobile connectors permanently problematic?
Mostly yes. I'm not sure if all brands of those mobile charging cables (like J1772 plug ones) also do that ground test or not. If they do, then they would run into this same problem.
I've been charging my Model 3 for the last twelve months without problems. Cable runs from my electrical panel to a box with a GFCI, then on to a box that houses a NEMA 14-50 outlet.
It's worked flawlessly. No tripped breakers in twelve months.
Yeah, some people just don't have this problem come up if they happen to get a good GFCI breaker that stays within spec for a long time. But they are very touchy and sensitive, so the rate of people who do run into problems with it is annoyingly high.