I have never found it necessary to carry a firearm for protection. I think that it is ridiculous. When I lived in New York City we used to go to after hours clubs I Harlem to hear jazz and salsa clubs in the South Bronx. I had a girlfriend who lived in Harlem and used to walk her dog at 4 or 5 in the morning when we got home. I never felt the need to carry a firearm, and there was no need.
I never felt the need either, but know you are deluded here.
I lived in Ft. Greene on Ft. Greene Place in the 1980s. Only white dude on the block (nearby BAM). Neighbors who were white started moving in nearby. I told them be careful. Like you they were clueless. Heads bashed in with metal pipes and other robberies and assaults followed.
Knowing where you are, who is around and having the good sense to run or move away can save your life. I fit in most everywhere I've been, but I'm not like most people.
I was born and raised in the Waterfront district (Columbia Street) of Brooklyn (in the 1930s) and fortunately managed to end up in a Park Slope brownstone on Carroll Street. We moved to New Jersey when I retired in 1985 and while I rarely go back to Brooklyn I am quite familiar with the Fort Greene district you've mentioned. Having heard that neighborhood has been considerably gentrified I have no idea what it's like today, but before I left Brooklyn it was exactly as you've said -- a very dangerous place, especially near the Projects, and especially for Whites.
There are neighborhoods in Manhattan, Brooklyn, Bronx, and Queens where carrying a gun is the sensible option if it's available.
I had a neighbor (Richard) on Carroll Street who was a smart-ass 23 year-old teacher at Alexander Hamilton High School. I once mentioned in conversation with him that some of the students in that school were real bad-asses and advised him to be careful in that neighborhood he criticized my "insensitivity" and virtually accused me of latent racism.
No more than two weeks later I learned Richard had been mugged on Bergen Street while waiting for a bus after leaving an evening PTA meeting and he was in the Methodist Hospital.
As I said, Richard was a real smart-ass.