The advice about knowing your audience is sound .The thing is about these songs is that ,if they are good ,and if you sing them well , your audience will forgive you if they are music lovers and not attending a performance solely for political reasons.
There is often a lot of demagoguery mixed up with the singing of rebel songs - especially when drink is involved . I'm sure that would be the same in Orange circles. Performers have to learn to distinguish between whether audiences are appreciating songs for their political content or for their artistic merits . It can be both .
You should feel free to leave out offensive verses. I recall reading with horror the unexpugated words of the Irish(?)American song ,The Days of 49 , with all its racist verses . The song without those verses had always been one of my favourites. It's not so good nowadays as a social record of the prevailing racist attitudes in 19th century America because it's always sung with those verses ommitted , but it is better as a song .