I was told by coherence support that having things on different minor versions is "not really supported". They let you join them together to support a gradual rolling upgrade, but they really want them all on the same version.
That being said I've never had that issue that you are talking about with things with the same minor version since the protocol versions don't change in minor versions.
There is no source visibility so it is impossible to say what exactly changed between those versions - but it is unlikely that the protocol changed. (I'm not super familiar with the nuances of 3.5.3 - we were on Ye Olde Coherence 3.1 for far too long and then did a crazy jump straight to 3.7.1)