[release] Only push beta|stable on flutter

Bug: https://github.com/flutter/flutter/issues/125180
Change-Id: I25ab5a7b441deacd96ba222bc9f22e23150d4367
Reviewed-on: https://flutter-review.googlesource.com/c/recipes/+/42221
Commit-Queue: Casey Hillers <chillers@google.com>
Reviewed-by: Godofredo Contreras <godofredoc@google.com>
diff --git a/recipes/release/release_publish.resources/push_release.sh b/recipes/release/release_publish.resources/push_release.sh
index 6ebf923..028c77a 100644
--- a/recipes/release/release_publish.resources/push_release.sh
+++ b/recipes/release/release_publish.resources/push_release.sh
@@ -12,5 +12,8 @@
 git tag $TAG $REL_HASH || true
 git remote set-url origin https://$GITHUB_USER:$TOKEN@github.com/flutter/$REPO.git
 git push origin $TAG || true
-echo "##### PUSHING TO $RELEASE_CHANNEL #####"
-git push origin HEAD:$RELEASE_CHANNEL $FORCE_FLAG
+if [ $REPO == 'flutter' ]
+then
+  echo "##### PUSHING TO $RELEASE_CHANNEL #####"
+  git push origin HEAD:$RELEASE_CHANNEL $FORCE_FLAG
+fi