Christmas began as a religious celebration. Kwanzaa is celebrated in December. Hanukkah is also a religious celebration. Because they are all celebrated in December, someone could wish you Happy Holidays and feel they have wished you well, no matter who you are.
Also, Christmas has become much more than a religious celebration. It is also a secular event for many, many folks who may or may not be atheists. Christmas trees and stockings, presents and Santa Claus, families and cards, lights and shopping, have all become as much about Christmas as the birth of Jesus. You may not like for it to be this way, but it is.
You may honor Christmas as a religious celebration, but you can’t decide for others how they should celebrate the season. Schools, parks, public lands and buildings are for everyone so they need to be neutral.