... is that just going to bring ALL THE MONSTERS right to the party?

Specifically, one in the party has the Reveler's Concertina and Pipes of Haunting. I think that will at best mean that they won't be able to be stealthy, but, I feel like they WILL NOT be able to get surprise at all.

I guess if they close any heavy oaken doors they pass thru, that might limit the range of which the instruments can be heard...

"bluff, bluff, bluff the stupid ogre!" "what? rawr!!"

but, yeah, if you're thinking of a cave with connecting tunnels then the dm's going to have to insert an awful lot of racket in the kobold recreational area to keep them from marching out to see what's good. feeding time for caged beasts? engaged in a gambling game? maybe drunkenly seeing who can leave their foot in the fire longest? or perhaps they've got a peasant tied to a chair singing (poorly! like a complete amateur! (if that goads your bard)).

in a fort with thick doors the dm might hang some lovely tapestries to keep out the chill but also dampen noise. bard might still want to remember to say they're playing quietly on purpose. maybe the players stumble upon some of the equipment the fort captain hid away which necessitated additional sound proofing inside.

in a lonely forest it might not attract hungry wolves, but if it did then expect that it also called up some meddling fey. some pixies or such who don't care which side wins the battle as long as it is anything but boring. even better if a more powerful fey offered the little ones some potions to toss into the fray: one charms two combatants, confuse another, that one grows a creature large but blind, while three others polymorph into wasps, etc. ... and then what else hears this ruckus?

Oof. That is a HARD dilemma. Maybe discuss with the bard if he realizes that he will TOTALLY DEFFINITLY BE HEARD and it will ruin the element of surprise? I don't really know. That's a hard question.

I wouldn't worry too much. The sounds of music wouldn't need to really be any louder than the sounds of a fight generally. If the fighting would already draw an enemy's attention, then the instruments would. If the enemies wouldn't hear a fight, they wouldn't hear the instruments. Otherwise, it just seems like punishing the bard by saying they hear his song but not the explosion from the wizard's fireball, or the barbarian's battle cry.

With these specific examples, the concertina's big benefit comes just from holding it. If they use it to cast, then see above for how loud it gets. The pipes have a 30' range, so if someone is further than that, they might not hear them. So, yeah, I wouldn't worry.

I would say that if the bard walks around playing an instrument while going through a castle then yes, they will attract the attention of anyone that can hear them if music is out of place there. But so will any combat that breaks out. The shouts, stamping, blade against blade cacophony that goes on during a battle will also attract the attention of the dungeon's occupants unless they are really far away behind sound barriers. 

Just cast magic without music. ¯\_(ツ)_/¯ Bards can cast without music through things like poetry. 

The term "Bard" means poet or storyteller. They actually didn't use music. The medieval musician was a "Minstrel". 

Even using a musical instrument as a focus doesn't mean actually playing it - you just need to hold it in hand.

while i agree with the mechanisms and spirit of 'just don't play the instrument,' it doesn't have to feel good. smart but, i don't know, maybe too reasonable? if a bard in my party went about mostly waving a cheap flute like a wand or laying a hand on their cased lute, then i would be unshakably convinced the party had been infiltrated by an unsubtle spy of some sort.

Let the bard's player do what they want.

Warn them of the consequences beforehand and enforce the consequences afterwards. Anything else is robbing them of their agency.

I'd say that OP is underestimating how little noise travels when playing a musical instrument that doesn't have speakers in a place that wasn't built for optimal acoustics.

or the Bard can softy blow into the flute or pluck a string on the lute to produce a single note they can reference so they can be on key. They can then proceed sing the incantation, as one example. 

There is a school of thought that believes the verbal component of spell casting is not just as simple as reciting words. The voice of the caster may alter; booming and echoing to all who can hear it. Not to mention the sounds of the cosmos altering as a result of the incantation, and the follow up by the explosive nature of spell (not including the damage it may cause). 

Then the clanging of armor and metal weapons also does not assist in being stealthy. 

You are correct, that if the bard feels the need to constantly play an instrument while sneaking around then they will give away the party's position. No different than a fighter who bangs their shield constantly in preparation of battle or a cleric continuously chanting the praise of their deity. But during the course of an encounter, there are a wide ranges of things that will generate as much or more noise than Bard's instruments.