The problem is: in the case of New York City, "this particular" and "that particular" just happen to be egregious violations of God-given rights enshrined in the U.S. Constitution. You could be even more critical of Abraham Lincoln in this regard. He was a Republican as well. It didn't hurt his legacy. In the end, Lincoln was judged by the outcome, as all politicians are judged. So will Giuliani.
To some people, Lincoln's "outcome" was the destruction of the United States as it was established in the U.S., the loss of 600,000+ Americans in a stupid war, and 80 years of racial strife in the aftermath of his crusade to free slaves.
Lincoln's legacy is still a major point of contention, and has been largely established by northern liberals.