Revert "consensus: skip all messages during sync (#6577)" (#6654)

This reverts commit 13b95e7127.

internal/consensus/reactor.go

@@ -1197,6 +1197,11 @@ func (r *Reactor) handleVoteSetBitsMessage(envelope p2p.Envelope, msgI Message)
 // It will handle errors and any possible panics gracefully. A caller can handle
 // any error returned by sending a PeerError on the respective channel.
 //
+// NOTE: We process these messages even when we're fast_syncing. Messages affect
+// either a peer state or the consensus state. Peer state updates can happen in
+// parallel, but processing of proposals, block parts, and votes are ordered by
+// the p2p channel.
+//
 // NOTE: We block on consensus state for proposals, block parts, and votes.
 func (r *Reactor) handleMessage(chID p2p.ChannelID, envelope p2p.Envelope) (err error) {
 	defer func() {
@@ -1206,12 +1211,6 @@ func (r *Reactor) handleMessage(chID p2p.ChannelID, envelope p2p.Envelope) (err
 		}
 	}()
 
-	// Just skip the entire message during syncing so that we can
-	// process fewer messages.
-	if r.WaitSync() {
-		return
-	}
-
 	// We wrap the envelope's message in a Proto wire type so we can convert back
 	// the domain type that individual channel message handlers can work with. We
 	// do this here once to avoid having to do it for each individual message type.