That's because Suyin forced the issue by finding out who is on the ship and going there herself, not because Korra 'allowed' it.
Anyway, nope. The fight is specifically between Suyin and Lin. Everyone else is third party. Opal is collateral, but so is Korra, since Lin is letting her anger affect how she interacts with them as well (She did break Naga's ball). Opal was pretty much completely avoided until she directly confronted Lin. But if it IS her business, then Korra still didn't do anything wrong. Again, all she did was advise Opal. She didn't twist her arm to get there. Opal is the one who did the actual confrontation, so whether it is 'her business' or not. Unless your arguing that other people don't even have the right to speak their opinion on issues, Korra did nothing wrong.
But like I said, this is all bullshit. Lin is her friend, despite how much of a grouch she is. That makes it Korra's business to help solve any problems she can, if she chooses to. If she choose to lock the two sisters in a room until they resolved the issue, maybe you'd have a point, but all she did was go to Opal and said "Hey, you should talk, maybe you can work out what your mom can't." This is all she did. It's absurd to consider this an invasion of privacy. This isn't tactless, this isn't a threat, this isn't out of line in any conceivable way I can think of. That is being conciliatory. This is as respectful a contribution to help work towards a solution between the two sisters as I can think of.
Korra facilitated the meeting. Korra brought Opal to Lin. Opal desired to speak with Lin, and her desire was understandable. But from Korra's point of view, she knew Lin clearly had no desire to interact with Suyin nor meet Opal. Korra is actually incredulous that Lin wants to stay away from her family, but instead of opening a dialog with Lin to understand her motivations, she places them all in an awkward situation then scolds Lin for the fallout.
And I strictly disagree with the notion that because you are someone's friend, you can make their issues that don't concern you* your personal business. Lin made it clear what she was and wasn't comfortable with. And Lin's decision did not negatively impact Korra's mission to find new airbenders or to even recruit Opal. Yet despite all of that she made a call and it blew up in Lin's face. And further, Korra did nothing to help Lin through her personal crisis, which Korra is directly responsible for setting off in earnest.
Let me back up a bit. I understand that Korra should try and help people, especially her friends. But who was Korra actually doing this for? Opal expressed an interest in meeting Lin but would have gotten on fine without. Lin expressed an interest in not having a relationship with Suyin nor Opal, to the point of becoming openly belligerent. Korra does not even approach Lin to assess where her mind is at or give her the outlet she needed. It's reasonable to believe Lin would not have opened up to Korra, but at least the attempt would have been made. Korra could see that Lin would not be receptive to having her niece sprung on her, yet does so at the behest of Opal, who finds value in meeting her much talked about - yet mysterious - aunt.
To me this situations basically reads as thus: Lin does not want to do something, and Korra - not nearly understanding the depths of Lin's reasoning - does that thing anyways. The context surrounding this situation makes it understandable for Korra to want to mend this issue, but she goes about the situation in a careless way that hurts multiple people.
It's a relatively complex situation and you can understand the character motivations, but I hope that Korra understands her part in all this, and becomes more respectful of either side of a conflict going forward.
*People have their own personal things in life, and of course barriers are erected around them. Navigating these barriers can be a hassle, and becoming someone's friend does not entitle you to help assuage those barriers if said friend explicitly makes it known they want you to drop it. I don't think Korra should have never tried to help Lin get over her family issues, but it should have been a damn sight better than "I know you don't want a relationship with your family, but I think you're buggin, so here's your niece who's dying to meet you."
That's not what i was referencing.
I was talking the about what happened in the Great Divide.
I know. Which is why I said "I actually thought of..." to say that this situation made me think of a different situation than the one you were talking about.
Although Aang pulling a fast one to get shit done is a pretty interesting decision. You can chalk it up to him being naive that peace built upon a lie is likely to end in disaster, and a problem Aang will probably have to deal with later in his life.