Anybody who does not hate Jesus and what He taught should have the right to celebrate Christmas.
Q: Should Hindus celebrate Christmas?
A: Immediately upon conversion.
The issue is that there are two “Christmas” celebrations—one that is religious and one that is a part of the popular secular Western culture. Even most Christians celebrate in both ways, not purely as a religious holiday (though there are some who do).
We are non-Christian. We celebrate Winter Solstice as that is our religious holiday that falls at this time of year, on which we exchange gifts within our immediate family. We will have a special meal, pour libations to the Gods, read about the meaning of the holiday, etc.
We celebrate Christmas as a cultural holiday, like Thanksgiving or Fourth of July or Halloween. We visit friends and family for whom it is a religious and/or cultural holiday and celebrate with them, giving them their gifts at this time, as that is their preference. We do put up stockings for Santa, but that is the extent of our home celebration, unless my in-laws ask us to host dinner here, since they have no other relatives in the area.
We decorate our tree with ornaments that have family or religious significance to us, primarily nature and solar symbols. We ride around and enjoy all the lights and talk about the season of light returning. We read and tell stories related to the Solstice. We sing lots of seasonal songs, but usually not ones that are entirely confessionally Christian. We make crafts, bake cookies, buy or make presents, give to charity, etc (I have a young child). We have read some books about the Christian Nativity story so that she knows why some folks celebrate this as a religious holiday that is different from ours and knows what the symbols they use mean.
Things we don’t do–We don’t put up a Nativity scene, just as we wouldn’t light a hanukkiyah. We don’t demand that stores or groups not sing Christmas carols with a religious theme or not carry religiously-themed items, though it’s nice to find those that are more inclusive. We don’t get offended if someone says “Merry Christmas” or “Happy Holidays/Season’s Greetings” but we are more likely to say “Happy Holidays” ourselves, as we know from experience that not everyone is celebrating this as a Christian religious holiday.
It is important to us at this point, given the age of our child, to be clear on which is our religious holiday and which is a fun cultural holiday as she is still forming her religious identity.