Crossing the streams was initially discouraged, as Egon believed that “total protonic reversal” would occur: this effect would have catastrophic results (see quote above). However, in a desperate effort to stop the powerful Gozer the Gozerian, Egon noted that the door to Gozer’s temple “swings both ways” and that by crossing the streams, they may be able to create enough force to close the door on Gozer and its control. As the Ghostbusters cross the streams, the combination of that much energy closes the door to Gozer’s dimension and severs its ties to our world. The resulting blast destroys a good portion of the roof and blows up the Stay Puft Marshmallow Man.
In Ghostbusters: The Video Game, the Ghostbusters mention that “crossing the streams" during the Gozer Incident (events of the first Ghostbuster’s film) only worked due to the presence of a cross-dimension portal (a tactic which is referred to as the “Gozer gambit" by Ray) and should only be used as a last resort. During the game’s climax, the ghostbusters are pulled into Ivo Shandor’s ghostly realm and come face-to-face with Shandor’s Destructor form forcing them to resort to "crossing the streams" to defeat Shandor. The resulting blast not only destroys Shandor but also sends the team flying back to their dimension.
When Homestuck began, this game had not yet been released.
Seeing how big of an influence Ghostbusters had on Homestuck, though, I think this information might just come in handy later. You know, if anyone ever just so happens to be near a cross-dimensional portal and needs a powerful last resort to destroy an overpowered enemy, sever the ties between two dimensions, and return to their home dimension.