If you use two different master registries, I find that would be difficult to manage. (See mistake #2 for self-managed registries). The purpose of master.eligble=false on a second instance/cluster is that all ID registration events have a single source of truth. As the docs say, The Schema Registry nodes in both datacenters link to the primary Kafka cluster in DC A, so you would need to establish a valid network link between AWS and onprem, anyway.
Otherwise, with multiple masters, you will need to mirror the schemas topic if you want exact same subjects and schema ids between environments. However, this is primarily meant to be used as a backup, and you would eventually run into conflicting schema IDs for any producer in the destination region pushing schemas to the other master. Hence why the first diagram shows only consumers in the remote datacenter.
If you do not do this, then let's say you mirrored a topic from cluster A to cluster B, and the consumer used registry B in the settings, it would attempt to lookup an ID from registry A (which is embedded in the message), and that either would not exist or would be an incorrect ID for the topic being read.
I wrote a Kafka Connect plugin to work around that issue by registering a new ID in a remote master registry - https://github.com/cricket007/schema-registry-transfer-smt , though you said you're using MirrorMaker, so you would need to take the logic there and apply it to the MessageHandler interface in MirrorMaker
I've really only worked with one master, on-prem, and in AWS, the registry settings have Zookeeper connection pointing to the on-prem cluster settings.
And we don't mirror everything as the docs suggest, only specific topics. The purpose of using Replicator rather than MirrorMaker is that consumer failover is better supported, rather than simply getting data "over the wire", your clients are less dependent upon where they are running as well.
