As evidenced during the investigation of T211721, we don't just write session data to the sessions redis cluster, but we also write all data from anything in MediaWiki that uses MediaWikiServices::getInstance()->getMainObjectStash() to the local redis cluster.
This breaks in a multi-dc setup for a number of reasons, first and foremost that we replicate redis data from the master DC to the others, but not the other way around as redis doesn't support multi-master replication.
To fix the behaviour of the software in a multi-dc scenario, I see the following possibilities, depending on what type of storage guarantees we want to have:
If we don't need data to be consistent cross-dc: After we migrate the sessions data to their own datastore, we turn off replication and leave the two clusters operating separately
If we need cross-dc consistency, but we don't need the data to have a guaranteed persistence: We can migrate the stash to mcrouter.
If we need all of the above, plus persistence: We might need to migrate that to the same (or a similar) service to the one we will use for sessions.
I would very much prefer to be able to avoid the last option, if at all possible.