Play order:

Player A: Multiculturalism on Player C (Takes, say... cheaper Destroyers)
Player B: Cultural Crisis on Player A

The FAQ says that if Player B had Cultural Crisis 'd Player C first , that Player A can't target Player C with Multiculturalism , but nothing about if the order is reversed, with either target. Does an ability from Multiculturalism count as a racial ability for the sake of Cultural Crisis ? Does the original target player have to maintain their abilities for the Multiculturalism to continue?

If Multiculturalism triggers first, then you can copy the ability. Then Cultural Crisis would come and "remove" the ability in the original race, but the copied ability still exists for the round.

So the answer is "no, the original target player does NOT have to maintain their abilities for the Multiculturalism copy to remain".

Think of it like a copy machine. If you make the copy first, you keep the copy even if the original is covered with whiteout afterwards. If you white out the original first, the copy will also be blank

Awesome, that answers half the question...

Now, the other half. Does the Multiculturalism survive a Cultural Crisis on its owner?

If not, then the "copy" is a Racial Ability. Not sure of the makeup of the Action deck, but that would mean you could Multiculturalism someone, then Cultural Crisis them, then have anyone/everyone else chain Multiculturalism off of the first Multiculturalism.

Now, the other half. Does the Multiculturalism survive a Cultural Crisis on its owner?

I believe Sigma already answered this. If you copy the ability first and then the original is whited out, you get to keep the copy.

If not, then the "copy" is a Racial Ability. Not sure of the makeup of the Action deck, but that would mean you could Multiculturalism someone, then Cultural Crisis them, then have anyone/everyone else chain Multiculturalism off of the first Multiculturalism.

There's only one Multiculturalism in the deck. Although MC followed shortly by that one that lets you copy a previously played card could still get you two copies.

Now, the other half. Does the Multiculturalism survive a Cultural Crisis on its owner?

I believe Sigma already answered this. If you copy the ability first and then the original is whited out, you get to keep the copy.

Nope. Other way around.

I play Multiculturalism. Someone plays Cultural Crisis on me . I lose all my racial abilities. Do I also lose the ability I gained through Multiculturalism? Sigma's answer assumes the Cultural Crisis is/was played on the other person.