Select Build Variant menu item greyed out

Had the same problem. Switched to Android Level Level View and the menu wasn't greyed out any more

I found that the "Select Build Variant" menu item became available as long as I wasn't viewing the project-level build.gradle file. While editing the project-level build.gradle file, the menu option was grayed out. But if I opened a different file, for example a module-level build.gradle file, the "Select Build Variant" menu item became available.