While the topics of politics and religion are definitely known stirring up controversy, and that arguments often boil down to ideology and belief making common ground hard to find, I don't think it's healthy to view them as one in the same.
Religion is important to people's identities for different reasons than politics. Religion influences people through philosophy, spiritualism, and salvation. People are opinionated about it because is an intrinsic function of religion to be unwavering.
Politics is different. It's possible to know a great deal about policy, and still hold unwavering ideological commitment to a side because you understand the consequences of policy. Political decisions create dynasties and destroy lives. People's literal survival hinges on the decisions of politicians, and in a Democracy we all have to play a part in what direction the machine goes.
Politics directly affects people day-to-day in a way that Religion never can. The largest problem I see is that people view politics through the lens of self-interest. One group may want lower taxes so that they can better use and save their income, while others may want higher taxes to fund welfare and provide a safety net from extreme poverty. Neither side cares about what the other side has to gain or lose, they only care about their side. So then we end up with nothing but bad faith BS and crappy compromises.
Politics is important. We should work harder to understand where our neighbors are coming from and find solutions that benefit the most people, not just our people. Discussing politics deeply and knocking down social taboos is a good thing, and we should do it more, not less.
Religion, on the other hand, is not so important to debate. We should respect people's individual religious beliefs, but we should also learn to keep our differences to ourselves because our varying religious and spiritual beliefs aren't really up for debate. What I believe or don't believe is of no consequence to anyone but me.