If I blocked someone because of political-related posts, yet the posts keep showing up, what did I do wrong?

That's an interesting question. LTC Stephen C. provided an accurate response but I'm not sure that it's complete. Hopefully he'll return at my prodding to answer my followup... (if he knows). Yes, "blocking" prevents someone from responding to your comments. However, it does not stop RP from displaying their original posts (Links, Questions, and Updates), which begs the question: Do you see all posts or only those tagged in groups that you have checked off as having an interest in? I can't imagine that I see every such post of every member in RP. There are hundreds of thousands and I would guess that original posts number in the tens of thousands every day.

SSG Howard Fair, blocking keeps someone from posting beneath your discussion threads, comments and responses. It does not keep them from starting their own discussion threads or responding to others.

Blocking a user only stops you from interacting with them. To block a discussion from someone, you can click on the dots and select "unfollow {user ID}".