I would say there are some fundamentals in morality which are universally accepted so there should be no problem on that score. And even if not, there are principles on which morality is based so that is a good foundation to learn about.
To interpret the word "teaching" as meaning telling you what to do or think is incorrect. The is another thread about teaching the Bible where I commented that learning about something and being told it is right is another matter. I learned about facism, that doesn't been I was taught to be a neo-nazi. Children can be informed and come to their own conclusions based on facts.
To take the women in pants example I would say that 100% of schoolchildren were born in the women in pants era. If the education is valid for the world in which they live, that's close enough. Although following on from my previous point I would teach them that dress is an aspect of morality and look at various examples throughout history and today, including the veil. Discussion can include topics like why can a man go bare chested and not a woman. Who knows that may changes in the future (and before too long I pray..hehe). And knowing about the dress code of others (eg the veil) and to respect it may make the world a bit more tolerant. How many times in the west do you see cartoons poking fun at the veil? But you never see a cartoon about the woman wearing a veil at a funeral!