Tecumseh: Jews work on Chanukah. Voluntarily. When I went to Jewish school, there were classes on Chanukah. We had one day off, pretty much just a long weekend, and that was mostly so we wouldn't be too jealous on the non-Jews who got all kinds of time off for their holidays.
Chanukah is a minor holiday and is not subject to the restrictions of holidays/sabbath. Also, it is eight days long. Ya really think no one should work for eight days to celebrate a holiday the celebration of which does not traditionally involve skipping working?
See, to answer Fistful's question from a couple days ago, this is why "happy holidays" is mildly irritating. It creates in the general public the impression that they are somehow aware of/participating in Jewish/black/other culture merely by wishing someone a happy holiday. When I was practicing Jew, it made sense to offer me holiday greetings on succos, pesach, the high holy days, and shavuous. Not so much chanukah.
Also, not everyone celebrates the New Year on Jan. 1. I used to celebrate it on Rosh Hashanah (or the first of Nissan, depending on how one counts). Now I celebrate it at the beginning of Advent. And yet, I'm still fine with Dec. 31/Jan. 1 as a generally celebrated New Year's.
Also, Ramadan is twenty eight days long (I believe). I'm pretty sure that Muslims, in Muslim theocracies, do not skip work for a month.
And no, a day off does not qualify as an establishment of religion.