It is not my view as I am not an islamist. Islamists view women as inferior, that is pretty obvious to anybody who cares to look. If you think women are treated equally to men in the Islamic world, you are obviously not paying any attention. We have enlightened western values that people in the middle east do not share. I am certain that radical islamists think what they think about Merkel based on her sex. It is what they do. I have always suspected that at a least part of the reason Saddam Hussein invaded Kuwait and started GW1 is because he did not take our female ambassador to Iraq seriously enough. It is fine for us to have our values but when we send women and openly gay people to be diplomats in certain Islamic countries, we need to keep in mind that bad outcomes may result because many people in those countries don’t share our views.
But your argument is that we should choose our leaders based on Islamists being sexist. Thankfully, again, I’m quite certain that is not Trump’s view.
And our female ambassador to Iraq was communicating what she’d been told to communicate. It was what she said, not that she was female, that, if anything, contributed to Iraq’s move. Your argument makes no sense, since if Saddam didn’t take her seriously he would have had less reason to invade Kuwait, not more.
Once more, no, we should no more choose our leaders for communicating with the Islamic world based on their prejudices than we should refrain from depicting Mohammed in cartoons.