Mostly it depends on what they expect and how they treat me. A Christian who wishes me a good Yom Tov gets a “Merry Christmas” in return. Muslim friends get an “Eid Mubarak” because I know how happy they are at the end of their month-long fast. It doesn’t mean Yeshu ben Maryam was Moshiach or Mohammed was a Prophet. But if they are willing to do the courtesy of respecting my beliefs I do the same for them and acknowledge the name of their holidays.
The one that causes me real problems is the holiday which comes around Pesach. Its name is a corruption of the name of a “deity” and commemorates a story about her descending into and returning from the Underworld.