What Protestants Get Wrong about the Temple Veil

Protestants sometimes object that we shouldn't (or at least don't need to) ask the Saints and angels for their prayers, since we can go directly to God. After all, they argue, the Temple veil that once impeded our access to God is now torn... right? That argument, which is also used against the Catholic priesthood, misinterprets this critical moment in the New Testament (and ignores the quite different way that the Epistle to the Hebrews interprets the same event). So what does it mean to say that the veil is now torn?