Like saying "A Jew holiday" or "Jew buns", "Jew hair", "Jew hat", "Jew-jitsu"
"Jewish holiday" is probably better than "Jew holiday." (It may be different in the UK, but in the US we say "a female doctor" not "a woman doctor.")
Unfortunately, the word "Jew" has been used in a negative way by some in the past. (Unfortunately, there are even dictionaries that list one usage of "Jew" as a verb to mean "to cheat." Rabbi Shimon Schwab said we need to change that reputation until it's listed as "Jew (v.). To be scrupulously honest." But I digress.)
The American Heritage Dictionary discusses this; some on their usage panel even preferred avoiding "Jew" as a noun, e.g. "there are two Jewish persons on the council" rather than "there are two Jews on the council" (or something like that).
I suppose that the examples are meant as jokes.
And in jokes it depends who and how speaks the things out. And it also depends who is/are the listerner(s). I heard from a Rov, that if joking person upsets one of the listeners he makes himself liable, even if he didn't meant to upset anyone.
Rabbi Nachman of Breslov zz"l advises, that if person wants to cheer up himself or other with a joke, he should try that -
- the joke isn't rude.
- the joke isn't upsetting for other people
- he shouldn't make it in order to show off.
You wouldn't say "a black holiday", "black dreadlocks","black hat" (or well, you might on this one!), et cetera. Would I call it racist? Only if you used in a negative, non-jovial manner. Context and subject are also very important. There is a difference between saying to someone "I find religion fascinating and I've always wondered what those Jewish hats you wear are for and what they are called?" versus "Yo, where can I get a Jew hat?". Again, just use your best judgement. Most Jews love talking about our religion, so as long as you're respectful and honest, I don't think there will be a problem
So, my answer is, just use common sense and be sensitive.