Long ago, I got over being polite about it. I really don't like losing my concentration when I'm singing, whether it's a song that I'm learning or one I can do in my sleep. It just doesn't come out the way I want it to when I'm disturbed by someone's conversation.
Over the years, I've dealt with it in different ways. The first is to stare at the talker. If that doesn't work, I may stop and speak directly to him or her saying something along the lines of "Let me know when you're done. I'd like to finish this song." Other times, I guess I just muddle my way through the song and then depart.
A good sing with a good crew is simply great fun. Sometimes though, it's tough even when people don't talk. I've had people sitting next to me having great time singing a loud harmony that's totally off key. A very recent experience, and a first of this kind, I was singing in a room full of people. Some woman began to sing the melody with me. This created a couple of problems. It was not a group song with a chorus, it was sung a capella, and the rhythm was a little quirky. Well, this woman, I guess, thought she had it down pat. So she sang loudly and just a fraction of a second behind me. Drove me nuts, I had this alto reverb ringing in my head. I blew one of the verses, finished the song and quietly departed. It just wasn't a situation that I was comfortable singing in. I sure didn't feel I could tell her not to sing.
Other situations that need clear statements: I sing a lot of songs unaccompanied . Often there will be one or more people in a room who feel that they will help me out by playing a rhythm instrument, usually a guitar. The reason I sing the song unaccompanied is because the rhythms forced by a guitar or banjo are exactly what I don't want. I usually just stop and ask people not to play. Most singers who don't sing a capella have no idea why I wouldn't want a guitar behind me.
Wow, did I get on a soapbox or what?