On the production VM, do we need to stop the vSphere Replication to DR site before we can initiate sync for the HCX migration to cloud on the same VM? In other words, can both vSphere Replication (Production to DR site) and HCX Bulk Migration (Production to Cloud) be replicating at the same time on the same VM?
Yes, you would need to disable replication otherwise it will error with a message saying that replication is already present on the VM.
Yes you need to stop the vSphere Replication.