As a Brit, the expression "talking past each other" didn't bother me, but it might be due to it sounding like a literal translation of a similar (and common) German saying (aneinander vorbeireden).
I don't think this is what the OP's looking for. This is (to me) the same as "getting one's wires crossed" - we understand each other and have no argument, but somehow we're not both on the same page, so to speak.
An example of a situation that the OP needs to describe (and please correct me if I'm wrong) is where someone who leans to the left of the political spectrum is talking to someone from the right of said spectrum. They both understand each other, but neither of them is going to be swayed from their point of view by the other. Basically, they're both too stubborn to engage in a meaningful conversation about politics and should talk about something else.
Similar situations arise between people who support different sports teams, or who practice different religions.
- For Teachers