Scenario: You're building a model in your room. You've been building something incredibly intrinsic and you don't want to stop until it's finished. Your father comes in and begins to scold you for spending so much time on what he believes to be a "waste of time". Your sister overhears the argument and comes in to take your fathers' side, citing hazards from working with fumes. Your brother hears the commotion, comes in to check out the problem and compliments you on what you've built so far. Your siblings begin to argue between each other on their opposing opinions. Your mother hears the squabbling and defends you from your father. Both arguments veer away onto extraneous topics. You lose your concentration and break something crucial on your model. You turn to your family and blame them for distracting you. Probably saying something along the lines of, "This is your fault. You couldn't leave well enough alone. You all had to be a bunch of __"?
People who intrude without due cause or permission are interlopers. If the purpose of the intrusion was to deliberately interfere, then they could also be called kibitzers.
Busybodies is a group of meddlesome, prying, officious people.
Officious: Marked by excessive eagerness in offering unwanted services or advice to others.
This seems to describe your situation to a tee (exactly).
I can't add comments so I am using this section to tell you that you accepted the wrong answer.
As others have told you already, the best word to describe such behavior is busybody. If you don't want to use it, then meddler would be the best-fit.
But interloper or kibitzer aren't words that define what you are describing.
"party crashers", "hangers on" or "buttinskis" are all somewhat slangy but servicable words for that situation
Technically they are minding their own business, they are just minding it on your patch. If they were poking their noses into your affairs, I would call them nosey parkers. However, in your example they don't appear to be being nosey. So I would be more likely to say:
"This is your fault. You couldn't leave well enough alone. You came in here like a herd of elephants."?
Perhaps not in your scenario, but a group of people who don't mind their own business could be called rubberneckers:
a person who turns their head to stare at something in a foolish manner, esp. while driving a car.