There's three things that generally need to be agreed upon in order for people to agree on politics. The first is what events have happened, the second is what actions caused those events to happen, and the third is what actions should happen.
If the first is not agreed upon, then the second applies to an entirely different world (whether real or imagined) and is thus de facto also disagreed upon and so then agreement on the third alone is not enough to entail political agreement. This despite the fact that the question of what should happen is the core of political thought. If Person A believes scientific consensus and Person B thinks vaccines will make them spontaneously combust, it is difficult for any agreement on what should be to occur.
If the second is not agreed upon, then agreement on points one and three are again insufficient to entail political agreement. If people disagree with each other who or what is to blame or to be credited for an action, than even if they agree with the facts and on the general question of what should be done, they will disagree on how that applies to the situation. If Person A thinks billionnaires are to blame for unemployment and Person B thinks immigrants are to blame, it seems difficult to imagine these people will agree on what should be done about high unemployment.
And if the third is not agreed upon, it doesn't matter if people are in perfect agreement on points one and two. If one person thinks a certain outcome is great while another thinks it is vile, they have a core disagreement of goals. If Person A and Person B both agree that that a certain action facilitates genocide and they both agree on who is responsible, it doesn't make them at all close to agreement if one of them is against genocide and the other thinks it's great.
Of course, such scenarios are rarely so cleanly mapped in real life as I imply here. But I do think it is helpful to think of what the main parts of these three components are that are agreed or disagreed on to better understand political disagreements. This shows that political agreement requires much more than agreeing on the facts, and thus one should make no assumptions on how informed a political opponent is from disagreement alone. Additionally, people must also have agreement regarding causes to have agreement on politics, and understanding disagreement in this area is about understanding differences in how a situation is analyzed and evaluated. Lastly, we must not overlook the biggest hurdle of all: a fundamental difference in the priorities that people may have.