Hmm, I have seen arguments between the types. LOL I have been part of those arguments in the past. Oh boy, this is going to be long. lol
Let me see:
Light RP: In my opinion, if you are role playing, you should not talk football in public places. Fine to do it in our private home or via PM’s, but by talking football, you ruin the immersion of the role play, for yourself and for others around you. I wouldn’t even call your definition of a Light RP a role player. I also don’t think greetings or salutations in the game’s theme are necessary to be honest.
I would define Light RP as: One who does not talk about real life events in public, but otherwise goes about playing the game. They don’t have to be part of plots, or have a deep background or any of that sort of stuff. They just have fun and don’t talk about football or real live events in public.
Med RP: I would completely rewrite this one. 
This person stays in character, meaning they have some sort of concept for their character and they stick to that in the game. They are not weird or obsessive about it but if they are playing a character who was the youngest son of a big family and struck out on their own, they stick to that character concept. Like the Light RPer, they simply have fun with it and go about playing the game.
Heavy RP: This is a person, like you said who researches the lore and tries to fit into the theme of the world. Again, salutations to me are shallow and not necessary. Attempting to fit into the world and using the lore as props to enhance the role play is more important. Again though, the person should have fun and not worry if mistakes happen.
By the Book: I guess you might call these my Heavy RP although, one should not be obsessed about lore and about doing everything perfectly. So yeah, these people can be annoying but they can also be fascinating. If one wants to go ‘by the book’ and be perfect, fine but don’t expect perfection for those around you. As for the non-roleplayer or the light role player, they might really enjoy role playing with the By the Book person.
Elitist: The term elitist is usually a derogatory term given to the person by others. I think a better term might be Self-Absorbed Actors. I have met people like this. They tend to not really role play as much as create a very deep character, post their background stories all over the forums and elsewhere, and pre-create scenarios to act out with their friends. They expect anyone who plays with them to have read all the background stories and to be willing to be part of their story. If you try to role play with them and fit in any of the above categories, they tend to send multiple PMs telling you what they think you should do and how you should react or even worse, justifying their reaction to you by telling you their deep backstory. For many of us, this is no fun. It is not role playing, it is directing a play.
I won’t address the last one because honestly, it fits into all of the above. Role players, no matter the theme of their role play differ greatly, from light to obsessive.
As a role player, my style changes based on the game and the other players. I prefer to be a Heavy Role player. I read the lore of a game first, I try to fit my character into the theme of the game, but then I sit back and have fun. I do create a background, but I don’t want everyone to read it. I want to reveal my character bit by bit through the game play. I like to role play based on actions and reactions in-game, not on pre-created stories and scenarios. In fact, I hate those. They feel artificial to me. I like to develop my character through the game, not in spite of the game. I am perfectly happy playing with light and medium role players and in fact enjoy it very much! I like watching people grow and develop into role players.
Sometimes I am a light role player, sometimes medium, depending on the game. Sometimes there is no lore or the lore is very weak. If a non-roleplayer talks to me, I stay in character. If they ask my age, I use my character’s age. If they ask personal questions, I respond as my character. lol I don’t make a big deal about it and they probably have no idea that I am not a 19 year old girl, but that is not my problem. I avoid discussions about real life but I am not rude about it. I don’t ruin anyone else’s fun.
Keeping them all happy? Ha! Can you ever do that with any group of gamers?
My perfect game would be one where players are encouraged stay in-character in public. I don’t care if they talk among friends about football, but I don’t want to hear it in the tavern. I don’t want people asking if I am “really a girl”. Come on…don’t I look like a girl? Even if I were not a girl, why does that matter to anyone?
Unfortunately, as a role player, I have had some very bad experiences with people who really hate role players. They call us names, they attack our groups, even if we are non-combat, just because, and they do whatever they can to ruin our game play. They even brag about it on the forums.
This is the reason we are making our game. Not just so role players have a place where they ‘rule’ and don’t have to deal with as many jerks, but so they have a place where the game mechanics support and enhance role play.
