I feel the same way you do about Yuletide and its Christmassy connotations. It's not my holiday, but I don't feel excluded on that basis. But I'm happy to celebrate anything that doesn't require me to overtly worship a God I don't believe in, and which is open to participation by non-believers in the general spirit of celebration (and my favorite holiday is Holi, to which I have no connection whatsoever other than fond memories).

I like your menorah icon and I hate the thought of pre-emptively withdrawing it for someone's hypothetical offense.

And yes, Jews other than you do Yuletide! In fact I am pretty sure it was created by Jews.