There are more “Nursing Madonnas” in art than you can shake a stick at.
For most of history, breastfeeding wasn’t a big deal. Because that’s what they’re for. Ankles and waists and other things that were normally covered up were often racier. It’s not until relatively recently that breasts have been as hyper-sexualized as much as they are. So it’s a cultural thing, rather than a theological thing.
In the Sistine Chapel last year, Pope Francis sez—
“Babies have their own dialect,” he added. “If one starts to cry the others will follow, like in an orchestra.” He said that if the babies were “starting a concert” of crying because they were hungry, mothers should “go ahead and feed them,” for this too is a “language of love.”
and the previous year–
"As the sounds of crying grew louder, the Pope joked that the concert had begun. The babies are crying, he said, because they are in an unfamiliar place, or because they had to get up early, or sometimes simply because they hear another child crying. Jesus did just the same, Pope Francis said, adding that he liked to think of Our Lord’s first sermon as his crying in the stable.
“And if your children are crying because they are hungry, the Pope told the mothers present, then go ahead and feed them, just as Mary breastfed Jesus.”
But because it’s a culture thing, rather than a theological thing— you’ll have a variety of responses if you try it yourself.
Me, I never nursed in public, because it wasn’t something I was personally comfortable with. I always fed my baby in the car, or in the restroom, or wherever. But other moms were indignant that they were expected balance on a germy toilet to go feed their kid, just to avoid offending someone else’s delicate sensibilities.
Nursing covers or throwing a light blanket over everything are a good thing that straddles both worlds. Not every baby is happy eating with his head covered up, though.
So, if someone wanted to nurse in church, I’d probably encourage them to go to the cry room and do it discreetly, rather than sitting in the first row at church, fiddling with non-nursing clothes, and no cover-up.