The Catholic liturgical calendar divides the year into Advent, Christmastide, Ordinary Time, Lent, Eastertide, and Ordinary Time. As you can see, Christmas defines a good chunk of the calendar.

Hanukkah is nothing like Christmas and it isn't even a very important holiday in Judaism - in fact, it's emphasized so much in America specifically to compete with Christmas.

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In fact, there's a heck of a lot of stuff the Koran forbids but that Al Qaeda and ISIS do anyway. These groups have an extremely elaborate set of "justifications" for all this, but they all boil down to "everyone who disagrees with us is no better than a pagan, and none of the rules apply to fighting pagans." Both of these assertions are extremely controversial and are, to put it mildly, considered poorly supported by most serious scholars.

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Muslims do not ever worship Muhammad or anyone but Allah (God). This is Serious Business