I sing a lot. But then again, I have a toddler who loves music, so everything he does has a song attached to it. In public we are a normal non-singing family (except for the occasional singing along to whatever music is blasting).
At home, I sing at the table to get the toddler to eat, I sing when he takes a bath, when he goes to sleep, when he wakes up, etc.
So, the verdict is, no singing at the dinner table unless there is a toddler who won't eat without it!