Are Iraqi women allowed by their families to get married to foreign muslim men?

Yes Allah says you can marry ANYONE as long as the man has to be Muslim. If your a man you can marry any religion of woman but your kids have to take your religion(Islam) ....But Arabic families tend to stick to there culture too much and only marry Arabic men... Which is not a good thing. So it might be kind of hard for you. Good luck inshallah! :)