Is it offensive to celebrate another culture's holiday?

Or can it be done respectfully? I got to thinking about this because I really like Dia de los Muertos (as you can see from my avatar). It’s a more traditional celebration that pays respect to the dead, like All Saints Day. None of the young Hispanic people I know actually celebrate this- they just go out and get trashed like everyone else. There are parades, cool art, and activities like decorating sugar skulls, and yummy cakes. I’m asking this question because before I’ve celebrated this with a bunch of art students, whose attitude was, “Woah, that’s quirky and awesome!” without always thinking about the deeper meaning.

I’m of Middle-Eastern ancestry and not religious, so technically even stuff like Christmas or St. Patrick’s day would fall into this category. But those are so widespread in America that I know it’s fine. What about holidays that aren’t observed much in mainstream America? (Diwali just passed, too!)
So to sum it up: Is my enthusiasm offensive? Has anyone else celebrated a different holiday, and what did you do?