As I said, if you introduce additional rules, then the decisions of the characters would reflect those rules, because everything in their reality supports that. If the enemy henchperson you're about to interrogate is a member of the fighter's fan club, then that would be a relevant factor, which the characters should take into account.NPCs have a starting attitude of friendly, indifferent, and hostile. That attitude isn't going to be the same for every PC in the group. In many situations, the Warlock will be looking at a hostile reaction compared to a fighter looking at a indifferent or even friendly attitude. In many cases having certain PCs present might sour the social interaction.
This is the sort of thing that's going to vary significantly based on the setting. Sometimes, everyone likes paladins, or sometimes they hate them. Sometimes, everyone important is a wizard. Sometimes, there was a war going on, and now people look down on professional fighters. Unless you give them a codified class feature, declaring that people are nicer to them, class is a non-factor here.However, with all other factors being equal, a fighter is going to have a better starting attitude with most NPCs than a warlock.
Additionally, as far as 5E is concerned, your place in society is really supposed to depend more on your Background than on your Class. A warlock Folk Hero, or Entertainer, is probably going to be received better than a fighter Criminal.
To the extent which that's true, it's not relevant to the topic at hand, which is how the fighter class does not offer support for those things. Unless you're playing in a setting where everyone likes fighters, which is tantamount to house-ruling them a new class feature, there's nothing in the class which helps a fighter do something other than fight. Which would be fine, if nobody else had anything like that (because nobody really needs those things in order to contribute), but it leaves the fighter coming up short in any direct comparison.Stats are just not the whole story. Backgrounds, NPC attitudes, Roleplay by the player all are much more important than Deception/Intimidation/Persuasion rolls.