Alan Jacobs raises some interesting points on authenticity and rootlessness, by way of Salman Rushdie's reflections on his experience of living in London. He's right that it appears to be a common difficulty in finding and substantiating roots for oneself, and that being rooted in multiple things is often a source of difficulty. It's also not something I've had much of a problem with personally. I see no real contradictions or problems in being a midwesterner who lives in the south who is now living in a different part of the midwest; going to a Dutch Reformed or Presbyterian or Anglican or Lutheran church depending on where I am and what's available; subscribing to some idiosyncratic version of liberalism, conservatism, and classical liberalism; modern and post-modern, depending on the situation; a fan of realism in literature except when I prefer experimental or genre work. But then, I've always been a nominalist: there's only one me, and though I might belong at times to different categories, I do not exist only as an individual instance of them.
There's a music analogy for this, which is the rise of the contemporary hipster listener. My preference is for the grand narrative, the school of Christgau, of the rise of indie rock; I grew up in the 90s so it tilts towards Seattle alternative; I grew up in Michigan so I like hip-hop, though (unusually for Michigan) only of the east-coast variety; I read the music papers I got in the original Borders in Ann Arbor so I liked Britpop; I like country but only the right kind of country; my introduction to jazz was through fusion, which taught me a lot about dissonance, but all my favorite jazz albums are from the 50s, and are bop or cool jazz. These are all of them various orthodoxies and heresies, but the collection of them, while idiosyncratic, is in no way unusual. So also with identity all the way around: the preferred mode of most people I know, including the ones who strive for authenticity and identity, is to pick and choose those elements they like and discard the rest.