How do you develop cultural adaptability?

Be curious 

Don’t be afraid to ask questions about other people’s cultures.

This is one of the best ways to learn and much more up-to-date than reading a book. Put some thought though in to how and when you ask questions. Show that you genuinely want to learn about the culture and are not just asking so you can pass judgement. Make sure the person is in the right space to be able to explain things to you. Be sensitive. If they don’t seem to want to talk about it, don't push it.