No, it should not be encouraged to persist. Emphasis on encourage (or discourage), not ban. It is a matter of public debate. I don't think any of our neighbours despise us or think we were whores, even though some let their daughters little freedom. I think you overrate how often behaviour or attitudes like that occur.
FGM is criminal behaviour, and the suspicion of a planned FGM would lead to the removal of the child from the family--rightly so.  An approach of respect for different cultures is not the same as tolerating every behaviour. A conservative to reactionary attitude towards women's and girls' sexuality is not enough reason to remove a child.