There is no such thing as a "GMPC".
There are PCs and NPCs. A GM is not the same thing as a player - any character that they are running is, by definition, an NPC.
An NPC that is also a party member is fine, as long as the GM uses them as an NPC. The moment the GM starts thinking of that character as being "their PC" you have a problem. You should be telling the story - you get an infinite number of characters to play as GM, and the trade off is that the players are the protagonists...not the GM.
GMPC's do exist. They may be a
subset of NPC, but they are definitely in a category of their own.
If a GM has taken the time to create an NPC with the same level of CharGen detail as a player, and has inserted that character into the game with the same rights as all other PC's at the table, then that is a GMPC.
There are reasons this can work, and especially under a rotating GM scenario, it's quite reasonable.
Also, if there is a massive gap in the player skills, then a permanent GMPC fixture may be warrnated (although IMHO a normal NPC is sufficient for this, but different strokes for different folks...)
The problems occur if at any stage the GM
believed to be favouring the GMPC. When that happens, it's game over, no-one's having fun anymore.
Therefore, it's a
risk vs reward scenario. Is having the GMPC at the table, worth the risk of spoiling everyone's fun for what may be just a misunderstanding in the end? Normally, the answer is
Hell no, not worth it.