What would you call a group of people who don't mind their own business?

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