This is a bit racially charged, but I will try to give my opinion as delicately as possible. FYI, I am white and straight, but have been mistaken for gay by most people my whole adult life. I also am a native Houstonian and love the city. I think you will be just fine in Riverside Terrace, but I base that on my own experience and my comfort level when I am in a neighborhood where I am a minority. I have never lived in that particular neighborhood.
I can't tell you how to "behave" in your own life, but I might suggest, that you learn about and be very respectful of the history, traditions and current residents of the neighborhood you choose. This doesn't mean you have to give up any of your own identity, but be prepared to interact with people who are "different" than you are. Although its not politically correct, I think there are clearly some differences between blacks and whites, gays and straights, rich and poor, men and women, etc... Forget politically correct...the differences are what make us interesting and what makes city living rewarding!!!
Gay people and black people are both minorities and both groups have suffered oppression and discrimination in this country. That is something that you hold in common which I think is a good foundation for being tolorant of others (and each other). I think that is a plus. My experince in living adjacent to Freedman's town in Houston for many years and staying in Harlem in New York for many years is that the black community takes a great deal of pride in their neighborhoods. The problem is that there is frequently a lack of resources that the community has access to. So, the neighborhood frequently looks "bad" even though the community is tightly knit and looks out for each other. Like any neighborhood, there is always a risk of crime and in a depressed neighborhood perhaps moreso, but there is also the chance to buy much more house for less. I suggest you don't be afraid to try that neighborhood. That location is very nice and the value will continue to rise in my opinion.
Support the businesses, join the civic club if there is one, introduce yourself to your neighbors! If you make an effort to fit in and be respectful of the residents and businesses there, I think it will come back to you. Be mindful though...its the big city...which means wherever you are you should lock your doors, watch your back and not let your guard completely down.
One more thing...if you still want to consider other neighborhoods...you might take a look in Glenbrook Valley. We looked in Riverside Terrace, but opted for GV. Its a VERY interesting neighborhood with great 1950s architecture, a very active civic club and LOTS of potential. And, its CHEAP and 10 minutes from downtown. Good luck!!!