Question: As they say, "politics is the exercise of power", and "power is the ability to make things happen in an organisation".
I am working on a project which has some overlap and is partially in competition with other projects. Managers at all levels have different ideas about what should happen. I am trying to understand who is supporting whom, what are the networks I should be aware of, to have a clear idea of where support for our idea might come from.
My line manager doesn't want me to think about politics at all. Other people told me not to be political. But I think these people might have their own agendas - like everybody else. I have seen what happens when you work hard on a project, ignore the politics, and then get backstabbed by some unforeseen person or project.

I do believe that "ignore politics" is bullshit advice: whether you manage people or build things, politics will determine the allocation of resources to your team or project, but I might be wrong.
So, let's ask it this way: **"what are the circumstances when ignoring company politics is good advice?"**

Answer: 
But also: *what is* **your** *job?!"* 

"Politics" obviously surrounds "every single human activity." So – is this *actually* "a battle that you have to fight," in order to fulfill your business obligations to the company?

"If it isn't – *butt out!"* Do your job. Earn your salary. Dazzle your [internal?] customers first, and your managers second. Don't worry about the rest. *"It's above your pay grade ..."*
Your manager telling you to not think about politics is a political act. Which means he's told you not to think about that advice. You can't follow advice without thinking about it.

Nonsense is never good advice. Ignore this particular advice but don't be obvious about it.