Yes. There is a paper that shows that if a data type has non-commutative operations, then avoiding expensive synchronization is impossible
https://hagit.net.technion.ac.il/files/2015/09/popl168gf-att...
https://hagit.net.technion.ac.il/files/2015/09/popl168gf-att...
What I'm more worried about is that we will prove that 'interesting text merges' are not all commutative. Though one trick we keep doing in spaces where things are proven impossible is that we cheat by creating tools that disallow or discourage the intractable scenarios. That could, for instance, lead to a generation of programming languages with a strange file structure that makes most workflows commutative.
That may sound strange or terrible to some people, but it's been my opinion for a number of years now that most of our coding conventions boil down to issues of avoiding merge conflicts, so a language that enforced a stronger form of conflict avoidance would be an 'opinionated' language but within the realm of the sorts of things we already put up with. Maybe no stranger than pure functional or Actor based languages, for instance.