Don't register a tracing dispatcher if no tracing env var was set.

src/librustc_driver/lib.rs

@@ -1233,6 +1233,12 @@ pub fn init_rustc_env_logger() {
 /// log crate version. In contrast to `init_rustc_env_logger` it allows you to choose an env var
 /// other than `RUSTC_LOG`.
 pub fn init_env_logger(env: &str) {
+    // Don't register a dispatcher if there's no filter to print anything
+    match std::env::var(env) {
+        Err(_) => return,
+        Ok(s) if s.is_empty() => return,
+        Ok(_) => {}
+    }
     let builder = tracing_subscriber::FmtSubscriber::builder();
 
     let builder = builder.with_env_filter(tracing_subscriber::EnvFilter::from_env(env));