I think it's the shippers being convinced that everyone else was as fixated on the AJ/Kai 'romance' as they were, and that therefore he will be seen as a heartless cad by the public. But the reality is that nobody was that invested, and definitely nobody cares now.
It's the same logic the Rose/Gio shippers are using: saying that Gio needs to 'publicly' address the rumour (that they started) that he is seeing one of his dancers, lest Rose's reputation get tarnished. Meanwhile the Great British Public is like.. who??
I'm behind the curve here and although I looked on the DS AT, I can't see anything about this on there. How do they think Rose's reputation is going to be tarnished by not going out with Gio?! I would have thought exactly the opposite! I do think the public might remember Rose and Gio's partnership a bit more than AJ and Kai, partly because they won but also because that CC dance did make a big impression. But I doubt many were holding their breath for a romance after we were told she was in a relationship with someone else and definitely friend-zoned Gio a lot of the time.