The correct answer to this open question is the following.
The way in which we remain true to ourselves as we move in and out of different communities, cultures, and contexts is by really believing in our foundations and moral pillars that were taught by our parents since we were children. We need to be convinced that the teachings we receive and the culture we had since childhood is proper for our lives.
Of course, we have to maintain an open mind to acknowledge that other people and other communities have their own valid culture; the by-product of their own history and customs.
And that is the beauty of diversity. To have many different things to learn from and to choose from. If we like it and find it useful, we choose it. If not, we discard it. But always, with absolute respect.