Oh, goodie! A religion debate!
First, OP, your question, when boiled down to the essential etiquette, really doesn't pertain to religion. It's all about parental choices and your mother politely asked if a toy was appropriate and you replied that it was not. It is no different than a parent deciding that Barbie dolls, Brat dolls, violent action figures, guns, etc. are not suitable for their children. What a nice mother you have that she called to ask!
As for the thread hijack....I've known for years the history of celebrating December 25th and that the icons typically associated with Christmas have their roots in pagan customs. The Plymouth Pilgrims banned celebrations of Christmas in the belief that it was rooted in paganism which put them at odds with their less pious shipmates who wanted to celebrate it (read Gov. William Bradford's firsthand account in the book "Mort's Relations"). But I am also aware that since the 300's, Christians have been celebrating "Christ's Mass" on December 25th by attending Catholic mass and "Christ's Mass" has been observed as a religious holy day by millions ever since. I can see SamiHami's perspective but from an orthogonal view. Christians in 300-ish A.D. changed the name of a December 25th pagan holiday to one that reflected their Christian beliefs, i.e. Christ's Mass which over time was shortened to Christmas. Yet people today celebrate something quite different while still using the Christian name for the holiday. I personally believe the name of Christmas should be reserved for religious observance of December 25th and those wanting secular or pagan celebrations can opt to change to a name which better reflects their beliefs.
If one is not celebrating "Christ's Mass" but rather Saturnalia or Yule, then it seems confusing to refer to one's celebration as "Christmas" when it is really "Yule". Make sense? I think a lot of the confusion is over the semantics and meanings of the words. If you wish me a "Merry Christmas" or regale me with tales of your Christmas merry making, I think I could rightly assume you celebrated a Christian holiday. If you were to tell me about your Yule party or the family Kwanzaa get together, there is no doubt in my mind what you celebrated.
Perhaps this topic is better suited for the main blog. Anyone want to submit something for posting? PM me.