Is it appropriate to give university lecturers Christmas cards?
The religious connotations of word "Christmas" can be confusing and depend on the region. My UK university has Christmas and Easter vacations while most US universities now call these winter and spring vacations. In the US, a Christmas card implies a religious celebration while a holiday card is secular. In the UK, a Christmas card that says "Merry Christmas" would be seen as secular and the same as a US card saying "Happy Holidays". There are of course religious Christmas cards in the UK.

The level of appropriateness (or inappropriateness) of a Christmas card depends on the level of religiousness and the recipient. While I would not say giving a secular holiday card is inappropriate, it is pretty rare. I teach probably 500 students a year and I receive on average of 1 holiday card a year from my students.