Scientific evidence is in your own countries birthrate and breeding success rates. Assuming that this 'feminism' will lower birthrates via pro-choice technology and other 'feminist' ideals, then yes, less kids will die from the above mentioned diseases, since they wont even be born.. as it is today, across the western worlds. 

The planet needs a responsible, managed human population . Kids are dying in certain countries because growth and birthrates are out of control. Feeding and healing only results in more dead kids. Its a vicious cycle that needs to be broken in unconventional ways. Solve the root cause, dont treat the symptom

Which is why we need to stop immigration from countries that are 'out of control'. No point in rewarding and helping countries that cannot even manage their own populations by taking overflow citizens. Or maybe limit immigration to countries that practice feminist ways.. if we import too many misogynists, it will kill feminism here.. E.g. extreme religions