I think you're misunderstanding my point. I'm not disputing that the origin of the celebration is no doubt religious (note, I said 'religious' and not specifically Christian; I'll touch on that later in this post) but rather I'm stating that for many people, Christmas has no religious connotations at all. I'm sure there are a lot of people who do celebrate it as Christians, but personally I don't know anyone who celebrates the birth of Christ or refers to the Christian faith at all.
In most Western countries the holiday is a public one; we get time off work and schools are closed. But there isn't any focus on the Christian aspect and for a lot of people it's strictly commercial; you buy presents, you put up some shiny lights, you have fun and you eat food - that's pretty much it.
Again, I'm not denying that the message was perhaps poorly chosen, and I'm not agreeing with how the message was delivered. But those responsible for erecting the billboard have stated that the purpose is not to offend anybody religious but to highlight that it's acceptable not to go to church. The target audience (again, according to those responsible) are the people who have no faith or belief in the Christian religion but still feel obligated to go to Church by societal expectations and pressure. There is a documented and well-known tendency in many American states (notably, the areas in which the billboards have been placed) to assume that the Christian faith is the norm, and those who do not share the same beliefs are questioned and regarded as 'abnormal'. I have had discussions with Americans in place and they have been genuinely surprised when I've told them I'm not religious. The quote from the article reads:
So while the choice of wording is not ideal, some of the best marketing strategies are the ones that have shocked the readers and thus have stood out more.
I suppose that is true, in the same way that you have acknowledged Thor (the Norse god) forty-nine times this year. You also acknowledged Mars for a whole month, and even Julius Ceasar got his moment in the spotlight. Most things are named after something historic; Thursdays are Thor's Day, March is the month of Mars, the Roman god of war, and July is the month named after Julius Ceasar. So yes, in a way, we are acknowledging a lot of historical activities and people, which is pretty interesting.
Yes, the name literally means "Christ's Mass", but the holiday has a basis in a variety of religions. The meaning has been watered down like so many other Christian festivals, because Christianity has had a habit of absorbing the traditions and customs of other religions to make conversion easier and simpler. Christmas is actually adapted from the Winter Solstice - a festival found in many Pagan and even Roman religions - just as Easter was adapted from the Summer Solstice. The Christmas tree is a Pagan tradition, as is the use of wreaths of holly, etc. Therefore while Christmas is well-known for being a Christian holiday, it also has grounds in a lot of other festivals and holy days as well.
However there's a more significant point about the religious connotations of Christmas, and that is choice. I choose not to celebrate Christmas as a Christian holiday, because that has no meaning for me. It doesn't mean that I ignore that many religious folks do, it just means that I treat it the way I perceive it - a public holiday, time off work, and time to spend with my family, giving and receiving gifts and catching up with people I might not ordinarily see very much throughout the year. Those who are religious are absolutely free to celebrate Christmas by observing religious traditions, obviously, or in any way they saw fit - but if I chose to celebrate Ramadan or Eid al-Fitr then I would feel free to celebrate it in the way that I chose, of my own volition, and in a world of freedom of choice I expect to be afforded the right and respect to do as I please so long as my actions are not offensive or illegal.
Or I could say "Yeah. What are you? A pastaferian?". Or just shoot them with a paintball gun. 
