Technically, religion is a choice; but in practice it is usually as much a choice as one's native language. People who are lucky to grow up with access to scientific education and varied cultural awareness are more easily able to choose the religion they want (if any); but many people (I would dare say the majority, on the global scale) are only exposed to a single, often very narrow mindset heavily defined by "religion" (to which one can include formally non-religious mindsets, like anti-vaxxers for example). For them, it takes a lot of effort to change their initial programming, assuming they ever get a chance at it.
As for ethnicity, while again technically it is not a "choice", I'm not really sure it can be clearly defined. A friend was mine was born in Italy to British parents, his wife was Bosnian and two of their children were born in the US -- what is their ethnicity?