What is the point in having such _days_? Consequently, shouldn't we also have a Scientists' day, an Actors' day, a Plumbers' day, blah blah? Everyone has a place in the universe. All we have to do is never to forget our true calling.
In some cases the celebration is named after the activity (e.g. fighting cancer), but meaning is exactly the same -- would calling it "Programming Day" suit you better?
They are taken about as seriously as Programmer's Day in most of the world (ie. not much, most people have no idea they exist, even people in that profession).