TL;DR - MG EVs probably don't handshake properly with Tesla AC wall chargers (gen 2 and gen 3), despite the chargers being set to allow all EVs.
I may be able to provide some insight here, based on personal experience.
Firstly, I think we are confusing the two types of Tesla chargers: The Tesla Supercharger Network (DC fast chargers, like that pictured in post #4 of this thread) and Tesla AC destination chargers (wall chargers found in home garages, car parks, shops, hotels etc., sometimes on poles). The Supercharger network is slowly being opened up to non-Tesla users. But this is a different issue to what the OP is having.
I own a Tesla Model S, my partner an MG5 EV, and my mother and MG ZS EV. We also have a Tesla AC wall charger (HPWC as some people call it). And I have spent many hours trying to figure out why the two MGs will not charge properly with the Tesla wall charger.
I have tried both Gen 2 and Gen 3 Tesla wall chargers. You can Google the difference but they are both AC wall charges, the Gen 3 has a WiFi interface.
We had a generation 2 Tesla wall charger in our garage that I used with my Tesla for many years, no problem. Last year my partner got an MG5. The Tesla charger would not charge the MG. Then I discovered that the Gen 2 chargers have a dip switch inside them that enabled 'legacy mode' i.e. enabled charging on non-Teslas. In legacy mode I was still able to charge my Tesla, and our neighbour's Audi e-tron also charged without issue. The MG5 however was another story. Sometimes it would charge, sometimes it wouldn't and just sat there with 'Connected, uncharged' notice on the display.
There are other threads on this forum where people have tried different combinations of power car on/off, lock/unlock, plugin, reset charger etc.....i.e. the 'dance' as some call it. My partner eventually found a routine that worked most of the time. I can't recall the order of events. It was not as simple as just plugging in the charger as you would expect.
Then our 6 year old Gen 2 Tesla charger developed a faulty cable and would not even charge my Tesla unless I positioned the cable a certain way. I suspect it was a fault in the pilot/signaling wire.
So I asked Tesla about the Gen 3 chargers and they said that you can set them to allow 'All Vehicles' via the WiFi interface (as opposed to the dip switch on the gen 2). When I asked about MGs they said it will work with all EVs that are compliant with the Type 2 plug standards. I bought the charger, which was cheaper than many other chargers on the market and looks pretty nice, had it installed, and set it to allow all vehicles -----> no dice at all with the MG5. Grrrrrr!!! Tried my mum's MG ZS, same problem. Neighbours Audi e-tron, worked fine. Spent many hours changing maximum current settings, rebooting, enabling/disabling 'all vehicles', but could not get it to charge the MG5. It did charge the MG5 once, but I couldn't get it to do it again. I even updated the firmware on the charger, but still no dice.
So it seems that MGs don't like Tesla AC wall/destination chargers. There has been discussion and speculation as to why this is. One theory is that MG are not following the handshake time out regulations. The Tesla chargers expect the handshake (communication between the charger and the car as to what voltage/current/number of phases to use etc) to be completed with in a set time. But the MGs maybe taking too long to complete the communication, and so the charger times out.
This is not unique to Tesla AC chargers by the way. I read a couple of posts on here where people were having the same issue with certain Rolec chargers.
I have not found a solution other than my partner having to use the Granny (mobility) charger until we can get it solved.
Either Tesla (and Rolec) have very strict handshake time outs, or the MGs are taking too long and other brands of chargers are more tolerant. That is if handshaking is actually the problem. It certainly needs investigation because many people are getting caught out.......like the OP. Based on the fact that MGs seem to be the only brand of vehicle that I know of that can't use Tesla and some Rolec chargers is suspect the issue is with MG.
Marty, in New Zealand.
this year 
