Your skills dictate what you are good and bad at. And those are the sitck by which you measure all interactions with.
You may not be a world renown Hacker, but your character on paper may be.
Does that mean you will fail because you as the player cannot grasp the level of complexity of hacking NORAD's Mainframe?
No, not if your character is a hacking wiz.
So the same goes the other way, if you lack social skills in game due to your stats and skills, then you need to roleplay them that way.
If I have a low intellect toon, I play it to the best of my ability. And that means I even will do stupid things that get the party in trouble.
In the case of a low CHA score, I may say something inappropriate at a critical moment or during a dinner with high officials. Like on the lines of "WOW! look at those cans on that Felinoid! Oh, sorry. Didn't know that was your wife Mayor!" 'O_o'
It adds depth and some fun moments into the game.
If your DM wants to simply rollplay, then you probably wouldn't have come to the forums to ask your question, so we can rule that out.
Ideally, your DM will fall somewhere in the middle of these two. He will be interested in two things: what you want to get from the NPC you are interacting with, and what you will appeal to.
As a party, you can discuss this amongst yourselves. Then, your high-charisma characters can take the necessary actions to convey this. The players roleplay to the best of their ability because the roleplaying is fun, not because they are looking for a numerical advantage in the exchange, then dies are rolled with modifiers depending on the answers to those two questions.
So, if you are naturally inclined towards social interactions, you can still have input and your group benefits. But, when it comes to being the facilitator, your low charisma character should probably take a back seat (unless you want to risk the roll). Remember: the other players chose for their characters to be charismatic, while you did not.
(By the way, if we're having to roleplay our stats no one can roleplay even moderately high bonuses, because they're beyond the imagination and ability of humans. It MUST come down to description and implication at some point.)
For another thing, as pointed out, the mechanics cover this. They're the reason why it's not (or shouldn't be) necessary to be as good or bad as your character. This hinges on how the DM plays, of course, but if the weight is on the ability check, rather than the player choices then mostly the better characters will do better and it works out. If those players can't describe what they're doing to get those high rolls, the other players and DM should aid them.
It sounds like your DM penalizes or rewards characters based on the words of the PCs. Does he also penalize strong characters if they can't describe how they use leverage to lift a portcullis?
Anyway, so what if the low Charisma character is better in social situations?
Of course, this also depends on your actual skill values. The character might not have much presence but still be quite effective due to training and various other bonuses in a given charisma-based skill.
So, you might not be able to influence a nobleman or trick a guard, but you're just as much the life of a party as anyone else.
You might might know anything about religion, history, or magic, but you're great at accounting, not to mention planning and battlefield tactics (sans the actual powers of, say, a tactical warlord can grant), and you have a wide vocabulary.
The fighter player must bring a real sword to the game and swing it whenever he rolls to attack his enemy.
The rogue needs to take the DM's money from his wallet when he uses Sleight of Hand.
The druid player needs to bring his great dane dog to the game to represent his animal companion.
The wizard player must throw that dog's poo when casting Fireball.
If the cleric player cannot get Roma Downey or Della Reese to come to the game, he is forbidden to cast Greater Planar Ally or Gate for an angel.
The bard player can bring his accordion.
Otherwise, let a character's score in Diplomacy, Intimidate, and Bluff account for how well or not well the character uses those skills and ignore how well or not well the player himself can do such things.
It sounds like your DM penalizes or rewards characters based on the words of the PCs. Does he also penalize strong characters if they can't describe how they use leverage to lift a portcullis?
This is why I dislike enforcing a link between roleplaying and success at in-game actions. It is never done evenly across all skills (I doubt any DM would ever ask someone to describe how they are swimming), and unfairly penalizes people who are bad at certain skills for wanting to play a character who is good at them.
I do think it is fine to give out small bonuses for effort (that is, if someone makes an effort to roleplay, give a +1 or +2 bonus to encourage it). This will make people happy, encourage others to follow suit, and still won't make the dude with a 9 Cha better at diplomacy than the guy with a 19 Cha (or even a 16 Cha).
Some groups might like avoiding rolls altogether, but I usually prefer to include a roll. Certainly if the task is very mundane you don't need to have a roll (I would never make my players roll diplomacy every time they talk to an NPC), but for important things I think the roll is important. Without it, the very eloquent player with a character who isn't trained in Diplomacy and has a 9 Cha effectively gets a free skill (plus skill focus).