Merry Christmas Happy Holidays
This one is too much. If someone wished me a happy "whatever" day (that they celebrate, and I don't) I'd think it was just a nice thing. Getting offended at someone else's holiday is just being a jerk.
Stripper Exotic Dancer
Both words mean the same to me. Someone says, "exotic dancer," and I think, "stripper". Kind of like "car" and "automobile". I don't mind "erring on the side of what sounds nicer" for the dancers in question.
Fat Overweight
Technically, "fat" is a substance. I think it's right that "overweight" (an adjective) is used. Again, erring on the side of what's a little more appropriate isn't such a bad thing in this instance.
Black African American
White Caucasian
"Black" and "White" are easy, even if people are technically brown, light cream, sort of yellow-ish brown, or whatever color they are. Not all Black people have much of a link to Africa, and "African American" is just too long anyway. "Caucasian" sounds "technical" or "census-related" or something. I don't like the "technical" terms. I just think of myself as a White person.
Janitor Facilities Coordinator
This one is just stupid. There's nothing wrong with "janitor".
So, in answer to OP's question: Sometimes yes, but not necessarily always. 