Vanity, thy name is woman. 

The adjective "vain" has two common senses.  One of them applies here. 

It sounds like Motabariga is a sin of self-importance, the kind of character flaw that leads someone to believe that her (or his) appearance has a far greater value than it does in fact. 

Let's see how well it fits: 

The word Motabariga (which means something like vanity or self-aggrandizement) is the Muslim Sheiks' favorite word to describe a woman who wears revealing clothes.  The word has a negative connotation to it, and is used almost exclusively to attack women who dare to show more skin than custom allows. 

Vanity, thy name is woman. 

The adjective "vain" has two common senses.  One of them applies here. 

It sounds like Motabariga is a sin of self-importance, the kind of character flaw that leads someone to believe that her (or his) appearance has a far greater value than it does in fact. 

Let's see how well it fits: 

The word Motabariga (which means something like vain or self-aggrandizing) is the Muslim Sheiks' favorite word to describe a woman who wears revealing clothes.  The word has a negative connotation to it, and is used almost exclusively to attack women who dare to show more skin than custom allows. 

Edit:

I was wrong. 

OP asked for an adjective, but the one comprehensible example I've found treats the word in question as a noun: 

[My father is] ashamed of me and avoids walking with me in the streets because he does not want anyone to say his daughter is a Motabariga.

In that context, nouns like "slut", "skank" and "jezebel" are a better fit.  Better, but still not perfect.

The only perfect fit is no translation at all.  Instead, define the term in the body of your text:

The word ____ (transliteration: Motabariga) is the Muslim Sheiks' favorite word to describe a woman who wears revealing clothes.  This word, derived from the Arabic word for "to tower", means something like "a vain and haughty woman", and it carries a sharply negative connotation.  It is used almost exclusively as an attack on women who dare to show too much skin.

I agree with @BradC's comment.  The word and concept in question may well exist in that language and in that culture, but it simply does not exist in many English-speaking cultures.  If you were merely translating a narrative, a word like "jezebel" might well be a close enough fit.  However, since you're taking the time to discuss the word, you might as well make your discussion complete.