In a way it is good to “freak out” but only in the sense that it is good to be careful and use common sense no matter where you go to school. But the fact of the matter is that there is no reason to freak out about Tulane at all. One reason the crime stats for Tulane look worse than some other urban schools is that Tulane complies with the law to the letter and consolidates all reported crimes within a certain radius of campus. As I understand it, all schools are supposed to do this, but because of a lack of coordination between campus police and city police, they don’t. This can make the campus report look better than it should.
I know for a fact that crime against Tulane students within a 2 mile radius of Tulane has historically been lower than at a number of other urban schools, including U Chicago, UPenn, Johns Hopkins, Columbia, and USC; it is similar to Yale, Duke and several others. Schools that had lower crime stats against students when I researched this when my D was attending a few years ago were WUSTL, Emory, and Miami, although Miami reported a fair amount of crime against students when they were farther off campus, in the city of Miami itself. None of what I am talking about is student-on-student crime, which is generally confined to petty theft and the occasional bar fight. I am talking about armed robbery, simple robbery, etc. Violent crime against students is really pretty rare at all these schools.
I think the best answer to your question is that over the last decade there have been thousands of students attending Tulane, the majority of them women. The experience of 99+% of them is (serious) crime free and really great, because they use common sense. Again, I am not talking about bike theft and the like. My D would go out in the day alone for very long walks, but she would stay on main roads like St. Charles and Broadway, and not find herself in a more isolated situation. If she was with a few other people, then certainly walking just about anywhere near campus was fine. At night you should always be escorted by friends or call TUPD for a ride/escort. Even though most of the time nothing would happen because the area really is not that dangerous, it would just be foolish to risk it when there are all sorts of safety apps you can use to call for assistance and people are only too glad to provide it.
Any time anyone asks a question like this, for any college, it makes it sound like the day-to-day is much more dramatic than it really is. As any current student will tell you, this is not something they are concerned about in terms of occupying mind space, it is just something that you do as a matter of habit, no matter what school you attend. Definitely do not let this affect your choice, but instead just listen to what the safety people tell you and do it, every time. If you are going to drink, have a plan that someone is there to exercise good judgement. That will keep you out of several potential problem situations. If you find yourself alone at night for some reason, call TUPD with a phone app they provide or get a taxi quickly. That kind of thing. But just to emphasize, this will be the rare or never thing to happen to you. With common sense, you will have a normal and fun college experience, and Tulane and New Orleans are great places to have that. Actually it won’t be normal, it will be extraordinary compared to most schools.