Two thoughts here:
First, I think a key difference is whether we know the person who is sinning. If we know Tuiasosopo, then it's 100% our Christian duty to tell him he's out of line. But crucially, we really can't do that until we've shown him that we love him and care about him apart from this issue. I think if we stand from afar and tell someone they suck (or talk about them to others) then we're judging. But if we've shown someone we love them and want to help them do better because of that love, that's helping.
As far as the "do not be unequally yoked" verse, I'd argue that that's about not conforming to the culture, not about segregating Christians away from non-Christians. With Christ as our model, I think it's pretty clear we're supposed to authentically love non-Christians, and we're not supposed to judge them from afar and say okay we're not going to associate with you. You can associate with and love people without endorsing their actions or copying them.
IDK feel free to tell me this is mindless babble lol