Global human injustices feel distant to many people in countries like the United States because we are very unlikely to suffer from these injustices. We live in a country that is generally extremely protective of human rights and is quite tolerant. Because of this, it is rather unlikely that most of us will ever feel that we are in danger of having our human rights abused.
For a middle class American, global human injustices are likely to be something that only happens to other people. This is true even of non-white Americans and women so long as they are in the middle class. It is somewhat less true for homosexuals and some groups like Muslims. We live in a country where there are very few threats to our human rights. We tend to think that it is a big deal when the government wants to prevent us from having assault rifles or when it does not want to allow same-sex couples to marry. Without minimizing the importance that some people place on these things, they are not in the same category as things like the possibility of being killed for apostasy in Pakistan or that of being imprisoned for speaking out against the government in China.
In short, we live in a country where our human rights are, for the most part, very well-protected. Therefore, global human injustice seems like a distant thing to most of us in the middle class.