It's elections time in Pakistan and a number of Muslim contestants are advising people to not vote for a female or a non-Muslim contestant. Is there a specific Quranic verse that has barred Muslims from supporting a woman or a non-Muslim in the process of choosing a leader?
Non-Muslims should not be taken as allies or guardians by the Muslims, especially not in preference to Muslims:
لا يتخذ المؤمنون الكافرين أولياء من دون المؤمنين ومن يفعل ذلك فليس من الله في شيء
Let not believers take disbelievers as allies rather than believers. And whoever [of you] does that has nothing with Allah
ياأيها الذين آمنوا لا تتخذوا بطانة من دونكم لا يألونكم خبالا ودوا ما عنتم قد بدت البغضاء من أفواههم وما تخفي صدورهم أكبر قد بينا لكم الآيات إن كنتم تعقلون
O you who believe, do not take anyone as an insider but those from among your own selves. They would spare no effort to do you mischief. They want you to be in trouble. Malice has come out of their mouths while what is concealed in their hearts is still worse. We have made the signs clear to you, if only you understand.
Under shariah, non-Muslims should not be in a position of authority over the Muslims:
ولن يجعل الله للكافرين على المؤمنين سبيلا
Never will Allah give the disbelievers over the believers a way [to overcome them].
There is no verse in the Quran that disapproves of women in roles of authority, though there are hadith which disapprove of appointing women as rulers. Some schools of thought allow for women to be appointed as judges.