I'm not sure it requires philosophical agreement in all particulars in order to agree on practical consequences, e.g. an empiricist and a rationalist may disagree on epistemology but agree on the consequences of going outside on a rainy day without an umbrella.
Agree with the example, but philosophical disagreement will undoubtedly come on some matters, like almost anything that's debated in politics today. Example: on private vs government healthcare. What is the good that we are seeking? What is the value of the various tradeoffs that we inevitably have to make in choosing one system over another? These are philosophical questions. Only then can we answer the practical question of how we attain that good.
Or for private life, should I devote myself to getting as much money as I can, or sleeping with as many people as possible, or are there other good things I should pursue? These are philosophical; the answer will depend on our view of reality and of ourselves. Again, only then can you get to the practical question of how we attain said good.
In all these cases, and in the umbrella one, whether the consequences of belief X are good or bad will depend on one's view of said consequences. In the umbrella example, everyone happens to agree on the desirability of getting wet, but it doesn't help us in cases where we don't agree.
I agree that pragmatism probably isn't much help in resolving these kinds of ethical and political questions. It might be helpful in terms of focusing the discussion when arguments get excessively metaphysical or abstract, but if people disagree on the practical ends that should be sought or the best means of attaining them, then I don't think pragmatism can settle that.