There are a few women flying for Etihad and as far as I know they are all westerners. Western European, Irish, South American, maybe others also. I have heard of no issues arising out of them being female and as far as I know they are settled and doing well.
Americans are accepted in the Gulf but, of course, you may get some flak over the Iraq issue and USA foreign policy from many nationalities, which has nothing to do with gender.
Keep your house, for now, take a look at flying out of Dubai, Ey in Abu Dhabi or Air Arabia in Sharjah. Air Arabia actually had the highest percentage of women pilots of any Gulf carrier at one point, (maybe they still do) you work hard there though and lots of night flights.
Do not be discouraged, go for it, if it doesn't work out.....then leave.