I also decided not to register based on this requirement alone. It's not that I mind sharing my political view, or am perturbed that you asked. I simply do not identify with either party and was frustrated that I would be forced to classify my world view into a completely inappropriate selection. If you had listed libertarian, I would have selected that and not thought twice. Of course, there are plenty more political views beyond those 3.
It's not the fact that I care that people know which political party I choose to affiliate myself with, it's the fact that there is no apparent way to not choose. I'm not a Republican or a Democrat, don't force me to choose. A "decline" or "other" choice would solve this nicely.