|Adoration of the Shepherds by Gerard van Honthorst (1620)|
When Old English speakers wanted to speak of other people and their religion, Old English speakers would say demonym adjectives prefacing the word holiday.
To English speakers, other people and their other religions do not have holidays. They have days of significance to their religion.
Americans came to say the phrase happy holidays as a Christmastime greeting, which the sellers of Camel cigarettes introduced in advertising to Americans in 1937.