It seems the United States federal government's establishment of Christmas, a religious holiday, as a federal holiday would be illegal under the establishment clause of the First Amendment.
How is it legal? Or is it case of no one has bothered to change it yet?
It is perfectly legal and, many would argue, reasonable to have secular reasons to do something that happen to align with religious reasons. In other words, just because there's a religious reason to do something doesn't invalidate secular reasons to do the same thing.
The New York Times had an article in 2013 that explained the origin of the federal holidays in 1870:
Congress acknowledged that Jan. 1 is "commonly called New Year's Day" and Dec. 25 is "commonly called Christmas Day."
and further on in the article:
If you read the language of the [1870] bill, it's clear that Congress chose dates commonly celebrated as holidays by the American people, not for religious reasons but because of a history of recognition and celebration on those dates.
The federal holidays make sense from an efficiency perspective. If a significant number of federal employees will be taking those days off for celebratory purposes then it doesn't make sense to open federal offices if there's not enough staff.
Federal holidays only apply to federal employees and the District of Columbia. There's no requirement that your private employer, state employer or you recognize those holidays.
The answer is that it is not in fact a religious holiday. At least, as far as the government is concerned. The government doesnt presume or direct the manner in which you will spend the day...you can choose to worship the baby jesus or you can go bowling, or head out to the gun range to enjoy your precous second amendment rights...the govt cares not.
It is one of many examples of violation of the Constitution that is tolerated by the court for practical reasons.
According to the First Amendment "Congress shall make no law respecting an establishment of religion..." and Thomas Jefferson explicitly said that this means no law can prefer one religion to another, yet of course, this is exactly what making December 25th a national holiday does, because that day is sacred to Christianity.
Of course, by the same logic you could also condemn Blue Laws and all the various Federal laws that mandate Sunday and Saturday as holidays or having special significance.
This specific matter, and others related to it, have been challenged in the courts several times. I would direct those interested in this topic to the Supreme Court's Brief in Opposition of Respondents Jeffrey Niemer, Patty Hemsath, and Anne Dolan
The summary finding is:
The federal statute at issue in this case—which declares legal holidays on various days, including Christmas, and gives all federal employees the day off on those days—is unmistakably constitutional. Governments, always and everywhere, have marked in law culturally significant days and accommodated their voluntary celebration; culturally significant days, always and everywhere, include religious and nonreligious celebrations alike.
