I think that there is a difference between riffing in a song and alternating or not saying lines in the script due to your level of comfort. Riffing is just a way that an actor adds their own spin on a song. Yes, they are singing the song as written while adding something of their own into the mix. If, for example, you say gosh darn rather then Goddamn due to the fact that you feel uncomfortable because you think that your using the lords name in vein then that is different. There is a difference between adding your own little something to the mix and just alternating it altogether just because your not that comfortable with how it is written in the scrip.
I would think that any smart actor no matter what level of theatre they are doing, would know and understand that you're playing a character and the fun that comes with acting is when you get the chance to play someone that is worlds different from how you are in real life.
I was in a production of Carousel where the actor who originally got cast as Billy had to turn it down because he was a strong Catholic and didn't feel comfortable playing a character that not only beat his wife but got forgiven for such an act. I tol him that considering that there is a saint of actors, dancers and clowns I don't think that he would be offending his god. I also said that if his god was understanding then he would know that it was just a show and didn't reflect how the kid was in real life.
"If you try to shag my husband while I am still alive, I will shove the art of motorcycle maintenance up your rancid little Cu**. That's a good dear"
Tom Stoppard's Rock N Roll