But then they know the pill doesn't work, and will likely use a different form of birth control. In order for the mutation to spread, it would need to make the pill not work silently. And even that would be difficult, because women should realize the pill is not working because they're still menstruating.
women on the pill still menstruate
Only if they do the 3 weeks on, 1 week off cycle that is commonly prescribed. Women who continue to take the hormone pills can skip menstruation.
Related to the current discussion, women would quickly realize that their menstrual cycle is not lining up with the week of non-hormone pills.
The problem is that other forms of birth control all suck in one way or another. Your chances of successfully preventing pregnancy go down if you can't use hormonal contraceptives. That's why they were a big deal when they were invented.