As it seems the opinions regarding this particular question are split fairly even, I find myself throwing my hat into the ring just at the right time to balance the opinions somewhat. Acknowledging, of course, that each and every person comes to the table for their own reasons and in their own ways, I have to say that I absolutely fall into one category more than the other regarding the specific debate of character identity and its relationship to the player. As such, I’ll take the first moment here to respond to that.
Regarding character identity and my own personality, I will never deny that some characters are related to myself directly in some exaggerated fashion. For example, I have run characters whose identities are entirely based in the idea that I personally existed in the fantasy setting that is being used for the particular game. To be perfectly honest, these characters are absolutely not characters that I would ever wish to be or experience in reality and generally wind up being rather grim, but this is mostly due to my comprehension of the metaphysics involved and the ways that it interacts with a character in a completely different universe.
The majority of my characters, however, are only related to me in that they reside primarily in my brain. Any aspects of their personality that are not accounted for by accidental overlap (which happens to the best of us from time to time) tend to relate to my own self only as much as they would relate to any other person on the face of the planet. Just like with the NPCs I make for my games, these characters are all alive in their own right. They respond and act according to their own personalities and their own lives, completely independent of my own. This is not how everyone runs their characters of course, but it’s absolutely important to me to have that distinction. Especially given in-character conflicts that arise on occasion.
Even in the most lighthearted of games, you need to have a firm separation between your self and your character. Even if the character genuinely is a reflection of your own self, but I have absolutely had difficulties with this perception in the past as a DM. When someone makes the mistake of thinking that a character reflects the player in some fashion and that aspect of the character is conflict with their own who they relate to strongly, things can get very personal very quick.
I recall once having a difficulty wherein a particular NPC happened to share my first name and was somewhat central to events taking place in the plot. Given my clear personal religious devotions, it was assumed and stated on more than one occasion by one of my players that it was a self-insert messianic representation of Jesus and I was essentially using the entire plot to force the characters to follow Jesus (me, apparently) if they were to have any chance at stopping the BBEG from taking over the world. While this particular character did indeed happen to ever so loosely bear a resemblance to my self (mostly by the name connection) he was absolutely in no way, shape, or form to be connected in such a fashion and this line of relating a character back to the player is a dangerous line of assumptions that can both hinder in-game actions based upon even entirely mundane and innocent meta reasons as well as real interpersonal difficulties when someone reads a bit too much into a given character and “learns” something about the player that isn’t true at all.
Of course, there is absolutely no right or wrong way to approach your characters, but it seems a very strong point to never assume that another player has any kind of connection with their character unless explicitly stated otherwise. I’ll save my direct and personal answers for this prompt for a reblog of the original post, however.