I get particularly bemused when I hear claims that non-Christians are likely to be offended by the term “Christmas”. The same is true in relation to greetings such as “Merry Christmas” or the use of any traditional Christian imagery in relation to the festival (although of course most of the symbolism is not Christian).
That is because I have fond memories of my family exchanging Christmas presents with our neighbours in North London in the 1960s and 1970s. We were a fairly religious Jewish family and they were devout Hindus but it never occurred to us that we were doing anything offensive.
Clearly there was no question of either side trying to convert the other to Christianity. Both families were committed to their traditional religious practices. That included Jewish festivals for us and Hindu festivals for our neighbours.
The exchange of Christmas presents was simply seen as a gesture of friendliness and neighbourliness by both sides. And it was only natural that we used the custom of the wider community, of which we were both a part, to express our feelings.
A long time has passed since then but, from what I can tell, traditional religious communities have not generally changed in that respect. They are more than happy to receive friendly gestures from those of other faiths whatever religious imagery is used.
Those who nowadays rail against Christian influences seem to be projecting their own dislikes on to others. If they feel alienated from what is still, at least to some extent, part of the mainstream culture that is up to them. But they should not project their discomfort on to others.
PS – We also had two cats for much of that time.