It occurred to me that many people really do look at being Jewish as "doing mitzwoth." It's so foreign to my own perspective that I never really thought about it.
Mitzwoth are our clothes. A Jew is a Jew. Just like if you dressed up a football star in a cheerleader outfit, s/he could still play football. A Jew in any outfit is still a Jew. However, without all the padding and the helmet, the pompoms aren't going to protect him very much. Conversely, put a cheerleader in a football uniform and s/he doesn't magically know how to play football.
A non-Jew can do mitzwoth till they are blue in the face, but they haven't accomplished anything. A Jew without ever doing a formal mitzwah can change the world.
Of course if we are satisfied just being Jewish without bothering to perform the mitzwoth, there will come a time when we are embarrassed to discover we've been walking around naked our whole lives and never noticed.
(Sounds like Adam and Hava, no?)