Can a person live by the Dhamma and have another religion as well?
In short: no, you can't. Even cursory knowledge of the teachings of the Buddha and the dogmas of Christianity (or any other religion) will prove enough to realize these are irreconcilable. Just to give a quick example, take the Buddhist belief (one of the "Four Seals") that all things/phenomena are empty and devoid of self: this is enough to negate the whole of Christian dogma at once! There is no doubt that the view that Buddhism can be seen as simply a "way of life" stems from a profound ignorance of the teachings and practice of Buddhism, usually based on a feel-good, watered down version of the teachings that doesn't even come close to trying to get to grips with understanding something as essential as impermanence, interdependence, and emptiness.

EDIT: The above comment is not meant in any way to insinuate that non-Buddhists cannot greatly benefit from studying the dharma—far from it, especially when most Western Buddhists come from a (at least vaguely) Christian upbringing. It was only meant to express that truly abiding by the Buddha's teachings entails a worldview that is not fully compatible with that of the major religions.