Respecting the local culture of the visited country should be obvious. But for many tourists it is not. Here is an example: When I traveled to Cambodia with my parents in 2015 the newspapers were full of articles about the arrest of two tourists for taking naked photos in the ruins of Angkor Wat. (Read the full The Guardian article here.) The Angkor Archaeological Park is a world heritage site and a holy site to the Cambodians. Behavior like this offends and upsets them and it should be very clear to any tourist that this kind of behavior is inappropriate.
Respecting the local culture in terms of Sustainable Tourism also means helping to preserve the cultural heritage. Cultural heritage can be a lot of different things, for example historic monuments, traditional crafts or landforms and nature.
So as a responsible traveler you can do two things:
– Respect local customs and morals
– Support organizations that work on preserving cultural heritage