The reordering can leave at least a dead TokenFactor in the graph. This cause the linearize scheduler to fail with something like the assert seen in PR22614. This is only one of many ways we can break the linearize scheduler today so I can't say for sure that any of the other failures in that bug were caused by this issue.
I took the heavy hammer approach of just running the full RemoveDeadNodes function which will search for dead nodes. We might be able to be more precise and remove exactly the dead TokenFactor or detect that the dead TokenFactor even exists, but I wanted to start with the simplest fix.