The whole point of such thing as a "right" is that it is something that can get exercised without causing undue harm or danger to another person.
For example, I can call some guy who bumps into me on campus an asshole, without much chance of legal repercussion (besides maybe an ensuing fight). There, I am exercising my right to free speech - it does not cause him harm, or put him in any danger. If I shout "fire" in the middle of a crowded theater, I am exercising my right to free speech, but I'll be prosecuted and put in jail for a while because I put 60 or so people in danger and possibly caused them physical harm. (this is the obvious rebuttal to your conjecture about the person who likes to kill and rape people - besides, this is not a "view", these are actions, and there are obvious prohibitions against certain types of actions)
This billboard does not, as far as I can see, cause your brother any physical harm or put him in any danger. It may offend his tastes, but as long as it conforms to the community's standards of decency (another issue), he has little to no recourse. If your brother is openly against homosexuality, that is his choice. I know many people that do not agree with homosexuality or the lifestyle espoused therein. However, if he were to go out and physically rip apart two gay men kissing in a club, he would be infringing on their right to self-expression and (again) possibly causing them harm.