Those are mostly at a different layer. You can speak Thrift or Avro or Protobuf over stdio or HTTP or TCP or carrier pigeon.

gRPC spans layers, and it uses HTTP in a more intrusive way than even MCP does — it expects to own the entire URL space at the IP/port in question. Using gRPC in a nontrivial way for MCP would be fairly heavy-weight: you would probably need to set up reflection and figure out how to bind all the MCP calls to it unless you just use it as a tunnel.

I would prefer a core transport agnostic protocol, and then see MCP-over-HTTP being a spec on top of that.