Whatever you do, make sure your arguments are always from the point of view of the business side of things, that way, it translates to the work enviromentenvironment having a problem instead of the worker (read: you) being the problem: The problem is that loud political discussions are disturbing your work and making you less efficient (and everyone else as well, as they are discussing politics instead of working).
- The first step is to find out what your companyscompany's policy about this is; as most (at least large) companies have some kind of policies about political discussions in the workplace and/or about disturbing other employees work with idle banter and most of those policies say: Don't do it, keep it in your pants / do it in the break room.
It's obvious that if almost all of the people in the unit you work in share similar political views, such policies can be left unenforced, but if you find one, you can use it as leverage when you tell your manager (or whoever you end up dealing with) that this is getting in the way of your work.
Your manager being a part of the problem signals to me that he is not the best person to solve the problem for you (again, company policy is what you need to figure out first - who is the person you turn to when your manager is the problem / part of the problem / not fixing the problem, if you don't know, turn to HR and they will tell you who that person is, if you don't have HR, turn to his boss with a "I'm sorry to disturb you but I don't know who to turn to with this problem" -type of message explaining the problem as objectively as possible - don't blame specific people for it, just explain the cause-and-effect of it - and the need for a solution / policy). This might not be possible / work in a non-corporate environment, where policies and strict adherence to set rules are not so important and managers lead with a from-the-hip -attitude.
If your company has no policy on it or is very liberal about this, you can always get noise-cancelling earphones (or -plugs) and put 'em on while you work (personal favourite, I don't know how people can live without them in the modern world) or when the political rambling starts. Just remember to first find out if your company can supply them to you before making the purchase yourself (depending on the way these things work in your company, you may need to make a formal requisition either to your manager or to a specific unit in the company).