Q: Does the processor on my Hyper-V Replica server have to be the same as on the source Hyper-V server?
A: Hyper-V Replica works by asynchronously replicating the Virtual Hard Disks (VHDs) of a virtual machine to another Hyper-V server. In the event of a failover (whether planned or unplanned), the virtual machine is started on the Hyper-V Replica server. At this point the operating system checks the capabilities of the processor, which can be exposed to the operating system and applications. This means there's no requirement that the processors be the same on the source Hyper-V server and the replica Hyper-V server. You could use Intel for the source and AMD for the target. Because the virtual machine is effectively restarted, the processor capabilities are checked. You should, however, consider that if you have a lower-capability processor on the replica site, then the workloads running on the replica might run at a lower performance.
The confusion about processor similarity requirements relates to live migration, which is a different technology that's used to migrate virtual machines between Hyper-V hosts with no downtime on the virtual machine. Live migration moves the virtual machine without restarting it, so the processors must be the same or similar (if the Processor Compatibility mode is enabled) because the operating system doesn't restart and therefore has no opportunity to rescan the processor. This is an entirely different issue than Hyper-V Replica.