I used Amazing Grace as an example. The songs we sang recently were contemporary versions of traditional Christmas Carols ...both secular and Christian. Several people found the Jesus/God songs a turn-off as they were regarded as 'preachy'. We were not there at the venue we played to make any kind of political statements or to preach Jesus to the crowd. We were merely there to sing songs and have fun and involve our audience which, for the most part, we did accomplish.
I live in Townsville, Queensland, Australia. Since Christmas is summertime here - weird I know, I'm originally from Kansas, USA - Carols By Candlelight events are quite popular. There is definitely a move here, however, to curtail any perceived forms of preaching in public. That includes religious songs. We've never previously had any problems with the authorities regarding the singing of carols (other than being told not to preach ...not that we would) but more and more people are finding songs pertaining to Jesus/God as offensive. If there are enough 'complaints' to the City Council they may ban such events. That might be all it takes. Any time other than Christmas I doubt that we would be allowed to perform Christian songs in a public setting. Easter, maybe, but I somehow doubt it.