I actually have been thinking about this topic more than usual recently and I think it would be interesting to discuss.
One recent topic I would like to bring up that show how society is almost in a way inwardly racist without knowing would definitely be the media coverage and reactions of Americans to the ebola "crisis". At first, the coverage was normal. They were showing the situation in Africa where thousands of people were dying as would be expected. But then, once a white person got ebola, the coverage immediately shifted to white people getting ebola and totally ignored Africa. The coverage legitimately never ever went back. It could be argued that one of the people the news focused on was a black woman, so it might not be racism, but definitely a subconscious cultural bias in favor of the US. Another thing, the black woman I noticed was seen in a more negative light than the white people who were seen as brave and fighting for their lives and got tons of sympathy while the black woman was seen more as some dangerous bitch who was doing shit wrong and got ebola from her stupidity. I've heard this straight from people I know IRL.
The problem with subconscious racism is that it's not a tangible thing and is much harder to get rid of then visible racism. Someone could be racist in this way and not even know it. They could even hate racist people yet still have inward prejudices. Sometimes I fear almost to the point of paranoia that something I'm doing or saying is prejudiced in some way. One example I'm sure every white person has done and even non-white people have been guilty of, which is identifying non-white people by their race. Like using clothes or hair to describe a white person but then going "that one black dude" or "that asian chick". While I wouldn't say this is bad, it's still a small example of subconscious bias. Some more extreme examples are of course heavily debated which include the housing market and job applications which are huge cans of fuck I'd rather not open up right now. I'd be glad to discuss it in some replies though, just not this post.
Lastly, here's an example of subconscious racism I saw very recently that I find interesting. It's not the best experiment since there are plenty of confounding variables, but it's still strikingly true. (It also covers subconscious sexism which I'd like to talk about, but make a thread about that specifically if you want. I don't want the topic to be too broad. Stick to racism)