The most politically astute move for you is to focus on your job performance, so that no matter how your manager assesses your political opinions, he will have no choice but to positively assess your work.
At the same time, it is important for both of you to recognize that you are not going to change each other's political views, beliefs, or ideologies. Your political views are reflections of your deeper values, and they do not change easily or quickly.
The larger question is why the two of you are spending work time arguing over political issues in the first place. Although you may disagree on matters of politics, you both probably agree that the workplace is not the best forum for airing political rhetoric. This does not mean that politics should be a forbidden subject, but rather that the two of you should try to spend more time in the work arena, and less time in the political arena.
Having different political views is part of diversity at work, and such diversity can be a real asset. If political subjects come up, rather than trying to convert each other, it makes more sense to try to listen to each other, learn from each other, and respect each other's views.
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