The Catholic Church wants you to raise the children Catholic but you can marry someone of any religion you please.
The advice about a Catholic woman not marrying a Muslim man and moving to a Muslim country is not religious advice but good common sense advice that would apply equally well to Protestant, Jewish, Hindu, Buddhist, pagan tree worshipper or atheist women.
Yes, that is the criterion with Catholics: you must raise the kids as Catholics. I have a first cousin who gave in on this point so she could marry someone who wouldn't agree to it. When the family came to my daughter's high school graduation, which was in a Catholic church, one of her kids referred to the altar as "the stage."