If not mistaken, the initial complaint was that Starbucks was removing Jesus/Christianity from the cups, not Christmas.
Removing reindeer and/or snowflakes from a cup, has no representation to Jesus.
The special cups are red (with some green also). These are Christmas colors (so why all the complaints).
Christmas has mainly become a marketing holiday for retailers, and all they're concerned about is massive money/sales (not Jesus).
I am Christian, but this debate is all too silly.
Reindeer and snowflakes are of the Devil.