Sorry Henny Penny, I think you are wrong.

If it is a paid performance and the audience have paid money to hear and see you sing, then you should look at your audience and sing to them. Remember they have paid for you to entertain them. If you shut your eyes, it is tantamount to ignoring your audience and, IMO, bad manners.

In an informal singaround, maybe there is some leeway, though I still think it a little impolite.

Scrump has a valid point and calling him stupid does not make his point any less valid.

I have been a lecturer for most of my career before I retired last year and one point I used to make to students when coaching them in giving presentations was to look at the audience and speak to them. I think that is just as valid when you are singing.