From my recollection, at the beginning the singing at NI games was choreographed. Someone with a megaphone started the songs and the crowd joined in. If someone started a sectarian song, the guy with the megaphone would drown them out and start another song. After a while it became ingrained in the support that you just didn't sing certain songs. The megaphone is no longer required. To be fair it was a lot smaller crowd that we have at Ibrox so it was easier to implement. However it could work well at away games. I know someone from the Union Bears does this so the club need to work closely with them to come up with a plan.
The interesting thing is that it spread to most teams in the Irish League. For anyone who watched Linfield playing on Thursday you wouldn't have heard one sectarian song and their supporters are some of the hardest line loyalists around.
Having lived in NI all my life and like many others suffered directly from the troubles, it depresses me to hear songs about the IRA, Bobby Sands, the pope etc. Football is an escape and I love to hear songs about our team. There is also no problem with celebrating our culture.