Certainly, there is definitely a tendency for many people towards tribalism. They identify with the left or right on certain issues and then tend to adopt other issues also embraced by their "team" merely because that is what the "good" people believe, not because there is any real logical connection between any two given issues.
That said, one kind of essential difference I see between the left and the right might look something like this: The left over emphasise the importance of good intentions and under emphasise the importance of incentives. The right doing the opposite.
Having, over the course of my life, moved from a position where I was very much firmly on (what I would call) the left to a more nuanced position (although in many ways admittedly on the right), I remember very well how I used to view people on the "right" but now I feel like I've seen things from a different perspective. I used to always assume bad intentions from people on the right. Not merely that they were wrong and misguided, that they were cynically arguing from a position of self interest and really didn't actually care about how their policies would affect others. Now, more on the right I see people on the left as being naïve, wishful thinkers who's hearts are in the right place but who's ideas are wildly unrealistic. I feel like these attitudes are widely held and represent how the left and right typically view each other.
It's a weird asymmetry. At first I felt resentful of it. If we give you the benefit of the doubt, assume that you have the best of intentions, why can't you extend us the same courtesy? But the more I thought about it, the more it seems to flow from the left right distinction I stated above: The left over emphasise the importance of good intentions and under emphasise the importance of incentives.
Those on the right just don't care much about good intentions. The left care too much about it. Hence, if one has good intentions and someone else doesn't agree, they must not share your good intentions. It's something I've been thinking about anyway...