Let me presume sincerity in the original question and the follow ups, that there's a part of a piece that the performing artist finds offensive, or worries will be offensive to someone they do not want to offend.
As a person who performs a great deal of material as part of my current project (various words, mostly poetry, accompanied by a varied a range of music as I can muster) I run into issues such as this from time to time. There are several ways to deal with it.
1. You can just perform something else. There's a huge range of things to perform. We all must make choices as it's impossible to learn or work up everything. I can't tell you the things I don't perform, as they are of uncountable numbers, but as I look for material I'm naturally looking for things that attract me. Of course sometimes you love a piece, or think it's worthwhile, and yet you still have the issue.
2. Change the song. I work almost entirely with words in the public domain, and even outside of that I hold to the Folk Process, which says you can change any thing in any song for any reason, if you feel like it. Yes, you can be charged with bowdlerising a raunchy lyric or for being politically correct. How do I decide? I make the choice that feels right to
me. I know it's not politically correct to be politically correct is some circles, and so my choice may offend those. So be it. I cut for length or lack of interest too, and sometimes I just forget or mangle the words and keep the "mistake".
Though with in the public domain works I have every right to do this, and I'm in the tradition with the folk process, I interrogate my intentional changes all the time. Did I betray the author, if known? If I can't do the author justice, would it be better if I chose tactic #1?
3. Perform it in character or context. Art can speak the most horrible words and thoughts. This is not always pleasant to most audiences, and actually try to do this sparingly because I believe most people have enough suffering. Yet some of the richest roles in drama are men consumed by evil, and they must be played. And I love a good Child Ballad, and most of their stories are gory. We cannot forget or never depict evil or the tragedy-comedy of the human condition. Satire is one way to perform this, another way is just to use your acting skills as musical performer and bring out he inner motivations of the character.
Or perform more than one opinion, the Walt Whitman "I contain multitudes" approach. This is harder to do in the small format of the song, but easier to do in the context of a set.
4. If it's merely offense to the audience that worries you, ask yourself if that's you aim. Offense rarely teaches the offended in my experience, but of course offending one audience to attract another is a time-honored artistic stance.
Instrumental performers have it easy. The worst and audience will think is that your music sucks.
