Townes Van Zandt once said that he absolutely loves it every time he hears someone singing one of his songs, regardless of who it is or how they sing it. I think I would feel the same way, though I haven't written many songs and have never heard anyone else sing one.

But some people take the opposite position. I've heard that Samuel Beckett, who dictated every nuance of action in his plays, sued any performers who made even slight changes. That would make me not want to produce a Beckett play, even if I liked them, which I don't. When I wrote plays, I never included any action except entries and exits (as is the case with the texts we have of Shakespeare's plays), and I told actors to feel free to change any words to what seemed more natural to their portrayal of the character.

Even when someone writes what I consider a good song, they can still include a word or a note that doesn't sound or feel right to me. When I sing a song, I always make any changes as I see fit. And I probably make other changes that I'm not aware of, just because I don't try to copy something exactly.

However, I would not interrupt the songwriter while he's singing that song and tell him to make those same changes. That would be the equivalent to telling someone to change a painting hanging in their house. I agree with the OP that one should not do that.

I also would not sing a song with my changes in the presence of the songwriter, unless he asked me to, or said that he felt the same way about it as Townes. And I try to avoid doing it in the presence of people who know and love the song in the original form and would be offended at hearing any variation in what they're used to hearing; though in the latter case it's more a matter of not wanting to be around people like that than a matter of respect for the songwriter.