individual hostility vs. systemic prejudice

The crux of my confusion lies in the way that people who agree on the basic premise that social inequality exists and needs to be addressed sometimes fracture themselves by fighting about how to accomplish this goal, while the seeming majority blithely naturalizes inequalities, perpetuates systemic prejudices, and authorizes the erasure of difference—all while throwing out phrases like "that's gay" with impunity. As an activist, I’m not really sure where I fit into all this, or what my purpose is.

Anyone else have perspectives on these tensions? I have so many more questions than answers.