Have you ever heard of the "Three Ships to Success"? The one that is considered the best to have and/or demonstrate is Kinship. Kinship requires that you take time to nurture and build your relationships to make them stronger. The second ship is Sponsorship. This requires that a senior person in your organization take a personal interest in your career and your success. The third ship is Showmanship. This ship is your ability to delight and amaze your superiors, peers, and subordinates with your abilities and talents. While the three ships are important, without ability, skill, and knowledge the three ships will not take you very far.
While you work on your "three ships", keep in mind that if you work in a highly political environment you need to work on the following:
Don't criticize others.
Use data to back up your claims and don't exaggerate your needs or your customer's requirements.
Try to understand the political process where you work no matter how hard that may be.
Understand that many rules are out of date, no longer make sense, are not enforced, and are often ignored. Use this to your advantage, but never at the expense of another person, group, or your organization's reputation.
Prove yourself through your efforts, not by talking about what you once did.
Be respectful of others. Keep in mind they determine if you are treating them with respect, not you.
Be reasonable (this can be difficult). Note - I'm not sure who determines reasonableness.
On a personal note, I have never liked or performed up to my highest potential in highly political environments. The things I have listed above are weaknesses of mine and are things I need to work on to be a better project manager.
Remember relationships based on personal preference and personal styles are often major contributors to highly political organizations. Lastly, keep in mind the perceived and demonstrated values of your organization will drive the politics.
Rule of the day, the Three Ships of Success can help you to overcome political hurdles.