Christmas and Chanukah
Cross-religion education is a good thing, and I think most people would welcome serious inquiries from people of different faiths if they want to know more (or even attend services or other rituals). I've certainly participated on both sides of that and seen no problems. But I think we should remember that our religions are separate; they have different emphases and that's ok. We don't have to agree, and we don't have to try to build a lowest common denominator.
To my Christian friends, I wish you the best in your season of holiness now under way, as I know you wish similar things for me during the high holy days and at other times. I'm not offended by your observance of your religion; you don't need to water it down. Besides, the dreidel song is really insipid; please don't feel obligated on my account.
(Mind, I would have a different reaction to celebrations in a setting that's supposed to be neutral, like a public school or a place of (secular) employment. But that's not what I'm talking about here.)
[1] Some do not see a problem with things like singing Messiah. We all draw the "worship" line in different places.

part 2
So did I. We had a concert every year with mandatory participation. No one was trying to be mean about this; they just assumed that of course everyone was a Christian, and they really didn't know how to handle people who said they weren't. I'll grant that things are probably better now than they were in the 60s and 70s, but I'm not ready to believe that minorities feel on an equal footing just because someone threw a Chanukah song into the Christmas concert.
I'm just thinking that maybe we need to share our celebrations more, throughout the year. Maybe that would even lead to more understanding of each other and peace and harmony and good things.
I agree that sharing more would be good. I think it's safer to approach it as education or demo than as required participation, though. It's ok for me to sing you songs from my religion; it's a bad idea for me to lead you in prayer. I can teach you about the Pesach seder and invite you to observe one if interested, but I shouldn't hold one in the classroom. You can tell me about the liturgy of the mass and invite me to join you at one, but you shouldn't hand out communion. That sort of thing. We need to be careful not to blur that line between "observer" and "participant".
And not just because it makes some people uncomfortable. For some members of some religions, certain types of participation in other religions are understood to be sins. To you it might be a harmless concert; to someone else it might be worship. To you it might just be polite to genuflect upon entering a church; to someone else it is idolatry.
I used to sing in a (secular) choir that did a Christmas concert every year. When I told the director that I would be dropping out for the duration (and returning after that concert each year), she got upset with me. To her (also not a Christian, BTW), music is just music. I could not convince her that there might be a deeper meaning to songs proclaiming a god incarnate. Both of us were trying to understand the other's position but neither succeeded in getting through.