There are a couple of different issues here...
First, is the Game-Zero issue of what kind of game does Everybody want to play.
Do you want subtlety and intrigue, combat and spells, character driven, gritty realism, high fantasy, etc.
As a DM, you might 'overlook' people using a non-subtle approach -- and of course tailor the responses to the game the players want to play.
E.g. Ignore that they're being unsubtle and tailor the response as if they were slightly more nuanced than that...or let it lead to a confrontation, depending on what the player's would want to do.
Second, is the Actions Have Consequences issue.
In this case, describe what occurs using an un-subtle method of questioning.
E.g. People trying to sneak out the back door. Other people being antsy about answering. Getting partial answers. Basically, red-flags that things are going to happen that may not be 'good' for you.
I would also inject the NPC telling the characters that maybe this approach isn't the best one in a manner that they could understand...like the reference to the Lord of the Rings.
And let them re-think their actions...or mitigate them.
E.g. After initially barging into the tavern looking for Mr. X's contacts ham-handedly, the party tries to diffuse the situation be rationalizing their interest in Mr. X's wares and being too over-eager to cut a deal.
I would apply the idea that players don't want to do "stupid" stuff usually...although, occasionally they might...
The additional check the DM, to either explicitly "warn" a player that what they said probably isn't a good idea in-game (e.g. Did you mean that in character or out of character...indicating that maybe what you just said, you "really" don't want to do) or explain why something isn't a good idea using the rules (e.g. you don't want to move here, because you'll be subject to an attack of opportunity.)
Playerwise, I would allow a character to act in character...e.g. a rogue might be more subtle and streetwise, while a barbarian might be more intimidating , etc...And, have them possibly play out out their character's interactions.
E.g. A barbarian might walk in and try to intimidate people, while maybe not having great social skills. While a rogue might slink to the back corners and try to find the criminal elements. A bard might either look for social contacts or performance opportunities.
These, could be played as either RP opportunities or skill checks depending on the party/players...or a mix of both, RP and skill checks -- player describes approximately what they would be saying/asking, then the DM factors in anything 'relevant' (e.g. the player made a good speech/asked good questions or the NPC is suspicious/cautious) and makes a skill roll or rolls, then returns what happened.
As a DM, I would also base things off of skills and skill rolls and characters who can best accomplish skill rolls...and possibly have different characters learn something different based on skills and rolls.
Like, as above, maybe a bard character attempts to use their social interactions to track down a contact's information/current location. But, it's taking some time...and the barbarian is getting sick of waiting, so, after a while jumps up and says they are going to start smashing people/things to get things moving