Well, this makes me want to hit something.
Hark! the Herald Angels Sing." It comes from the book of the prophet Isaiah (9:6), rendered in the King James Version as "For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counseller, The mighty God, The everlasting Father, The Prince of Peace."
But there's a serious problem with conflating these two things.
The peace symbol (sometimes called the Footprint of the American Chicken) has always been a hateful sign to me, as there was never a doubt in my mind that it was anything other than the flag that Americans who hated America pledged allegiance to because they knew that if they actually flew the flags of America's actual enemies they'd get a pop in the snoot. The sign originated (according to Wikipedia) as part of the British nuclear disarmament movement, which, however good or bad you may find the cause or the people behind it, must be considered a political movement.
As I've gotten older I have come to respect the opinions of genuine pacifists, people who would not punch someone even to defend themselves, but I think they are as foolish as anarchists, in that they know painfully little about human nature. If you want to say that you have declared peace with the world and will not fight anyone, great. But most Christian denominations do not expect you to roll over and take it in the face of violent threats. Nor, do I expect, do most people who hang out peace signs. (Generally these days I take the peace symbol as a form of virtue signaling anyway.)
In John 14 (KJV again), Jesus tells his disciples, "Peace I leave with you, my peace I give unto you: not as the world giveth, give I unto you. Let not your heart be troubled, neither let it be afraid." That is very different from saying they will have peaceful lives, and for the disciples, then and since, they sure didn't. What Jesus is saying here has deep roots in the Old Testament, and means a good deal more than "No one's going to hurt you" (which it doesn't mean at all) or "Don't go getting all fisty out there" (which may be part of it but only part). Peace in the faith is itself a massive subject, a lot more than just the absence of fighting, and more information can be found about it here and here (and of particular interest, C. S. Lewis's "Why I Am Not a Pacifist" in The Weight of Glory).
But I don't want to get into all that -- Christians always pray for the literal kind of peace, as in no fighting, and like everyone else I'm glad we've never seen the need to drop atomic weapons all over the joint. These are right and good things to pray for. The point is that the peace symbol is a political symbol, and thus is the mayonnaise in the punch bowl of Christmas. I think the peace-wreath people are not happy to see American flag-based Christmas decorations, and for the same reason.
The fact is, Christians believe or ought to believe that politics will not save us; we're told to pray "Thy will be done," rather than "Let the 2017 Omnibus Spending Consolidated Appropriations Bill Pass Intact." As Mark 12:17 tells us, "And Jesus answering said unto them, Render to Caesar the things that are Caesar's, and to God the things that are God's."