Veils once were mentioned in canon law. This is no longer the case. Certainly there is no longer a small-t tradition of wearing veils as there had been.
Oddly enough, today the veil causes the **opposite reaction **of what was intended. It calls attention to the wearer. If modesty is the intent, it can’t be accomplished with an item that makes one stand out in a crowd.
A veil, for example, is only an option in childrens’ First Holy Communion in our parish. I can imagine some parishes forbidding a veil for the sake of uniformity in the appearance of the girls. I can’t imagine a parish mandating the veil.
I think in the United States there will be several possible reactions to a veil:
(a) “what’s that about?”
(b) that person is very old-fashioned.
(c) a sign of piety
(d) a sign of defiance to the Mass of Paul VI, Vatican II, the current bishop.
My reaction is to believe (c) in any case.
From my blog a picture of Jackie Bouvier while she was dating Senator John F Kennedy.