They do - frequently and often. If you see a deep and non-personality based conflict it means there is a political disjoint within the company - the incentives for either side are misaligned - either because one or both sides have lost contact with customers and that having to clearly and logically spell out the disjoint is raising up a political problem the hierarchy is unwilling to deal with.

In short, if we don't address the difference in strategy represented by the Sales Director and the Operations Director then when the two different strategies and priorities are given to a programmer to implement - we can blame their kvetching on "IT guys"'instead of the two directors.

As for a solution: I would abandon Agile in such cases (!) and ask the board of directors onto a two day coached off site where we will address the issue. And suggest everyone polish their CVs in case.