Yeah, it's not my intent to make what amounts to an ignorant comment. My thought has always been that Cinco de Mayo and St Patrick Day celebrates cultures - not blatently stating that it's a "country" celebration.. The title of this parade, from an outsider looking in, doesn't seem to emphasize the culture, but rather the country.
Around my area, we have the Polish Day Parade. The point to celebrate the Polish culture. In this case, calling it an Isreal Day Parade seems to bring the country as the subject, not the culture and not the Jewish religion.