Some of your answers left me with more questions, if you don't mind.
What are intellectual racists (aside from seemingly an oxymoron) and race realists?
Race realists and the like believe that biology divides humans by race. They like the bell curve, and/or try to find ways to divide races amongst one another by abilities and behaviors.
I sometimes refer to statistical racism, which I feel accurately describes people who use statistics to form racist opinions. "Many impoverished high crime areas tend to be filled with high a population of black people" becomes "a large portion of black people live in high crime areas" becomes "black people commit a lot of crime" becomes "I see a black person over there, that criminal better stay away from my family."
Stereotyping. The media also reinforces these thoughts. You may never meet a black person but you still have a mental perception of them. A race realist will try to use crime statistics to show that blacks are genetically different than whites, and that these statistics and associated behaviors are unique. But it's all bullshit anyway.
And I'm still lost on the difference between advocacy and verbally opposing racism.
In real life I go to events and occasionally meetings showing support. I am open to expanding my world view, and read up on history. I support targeted policy, and won't knowingly vote for someone who supports regressive policies.
Verbal support is not engaging in racist behavior, not being antagonistic, treating people by the content of their character, and thinking about confronting that racist family member, and sometimes you do, but ultimately you prefer peace than hostility. Or you may feel like you treat everyone equally, but don't worry about regressive policy too much because it doesn't affect you. You'd possibly vote for someone who does to get other things, but may not be racist yourself. Generally you treat people as equals, and while no one is perfect you're willing to speak up, but won't exactly shake things up.
I'd hope there wouldn't be many alt-right posters here, at least if means what I've come to think it means. In my view, the definition of the alt-right seems to be genuinely racist conservatives. Or would you say that's somehow an over-simplification?
The alt right embraces implicit or explicit racism, or even white supremacy. They tend to feel that mainstream conservatives do not advocate for the interests of white people enough as a group, and act too PC. On the surface level they're race infused, where as the conservative mainstream act race blind.