And when I use the same config :

\"proxy-rewrite\": {
      \"headers\": {
        \"X-USER-ID\": \"USER1-ID\"
      }
    }

In the route config it works :

curl --location --request PUT
"http://$APISIX_URL:$APISIX_PORT/apisix/admin/routes/api-v1" \
--header "X-API-KEY: $APISIX_API_ADMIN_KEY" \
--header "Content-Type: application/json" \
--data-raw "{
  \"uri\": \"/v1/*\",
  \"host\": \"$APISIX_HOST\",
  \"plugins\": {
    \"key-auth\": {},
    \"consumer-restriction\": {
        \"whitelist\": [
            \"user1\",
            \"user2\"
        ]
    },
    \"proxy-rewrite\": {
      \"headers\": {
        \"X-USER-ID\": \"USER1-ID\"
      }
    }
  },
  \"service_id\": \"api-v1\"
}"

I mean that when I configure the plugin proxy-rewrite on the routes I have
the header X-USER-ID set with the value USER1-ID (everything is fine) and
when I configure it on the consumer user1 and I call the endpoint with the
apikey of user1, the header X-USER-ID does not exist.