You often hear many people, including women, feminists, etc referring to a rape culture. If you live in a society that is very misogynistic which trivializes rape, or punishes the victims, or makes the victims targets for more abuse, then yes It's very plausible and even likely that islamic cultures in particular (but also western cultures) can have very big impacts on the degree of rape that is present.
These cultures are heavily influenced by their religion, and to deny that is foolish.
Islamic cultures in particular routinely treat many of the women like cattle. Many of those countries justify the use of burkas because otherwise "men wouldn't be able to control themselves." If you are a women and raped, your family may disown you. In some of those cultures, you may be forced to marry your rapist, or you could be simply killed by your own family members. There isn't much incentive for victims in these countries to even come forward.
So to answer both your questions, yes, I do believe that such a difference could very easily close that gap, and yes, I do believe the religion, which directly influences those cultures (often being the primary influence) permeates their society, and has a very big effect on rape statistics.