Almost all companies are heavily political. It's inevitable given human nature in hierarchies.
When people say "I'm not political" they're really just confessing to low social status and acumen. I personally wish things were different, but as you note they're not. So one may as well accept reality and play the game as best as one can. One can have a very successful career as a follower if one recognizes the traits of good leaders and the traits that good leaders are looking for.
Right. Politics is a tool often used to keep people with low social status where they are.
Much like gossip, politics is pack violence and order by other means, and is usable by people who have less physical power but more social influence. If you don't have either physical and social power, then you're dismissed as not a threat and ripe to be stepped-on. Gossip is often a political attack technique to take-down a physically-strong leader.