Yes, Christmas is a religious based holiday. However, the Christmas celebration of most people around world as well as over half the US is not based on Christ. Christmas was traditionally a Christian festival celebrating the birth of Jesus, but in the early 20th century, it also became a secular family holiday, observed by Christians and non-Christians alike
About 25% of Jewish families do Celebrate the holiday in some way, maybe a Christmas tree, lights, and/or exchanging presents but there is no religious significance placed on the Holiday. Many Atheists do celebrate Christmas as a family tradition like those claiming to be Christian but do not practicing Christianity in their daily lives.
In Japan, Christmas is celebrated much the same way we celebrate Valentines day. In China, Christmas is not a national holiday but it is celebrated. You'll still see the malls and streets of the big cities filled with Christmas decorations, fir trees, Santa Clause. It is more of a lighthearted day for going out with friends, rather than gathering with family. Instead of going to church, locals like to go shopping or ice skating, or head to karaoke bars and cinemas. Young couples can also see it as a romantic day for gift giving and expressing their love for each other.
With only 32% of the world population being Christians and only half being devout it does make sense for major businesses or government to promote Christianity or any religion. What some Christians see as a war on Christianity is simply businesses and government refusing to promote any religion. So when a school district or the city says no nativity scenes they are following a policy not to endorse any religion. It is not a war on Christianity rather it is being fair, not promoting any religion nor religion itself.