diff --git a/cibuildwheel/linux.py b/cibuildwheel/linux.py
index 7e71bbae..ce1bc057 100644
--- a/cibuildwheel/linux.py
+++ b/cibuildwheel/linux.py
@@ -65,7 +65,7 @@ def get_python_configurations(
     # and match the build/skip rules
     return [
         c for c in python_configurations
-        if any(c.identifier.endswith(arch) for arch in architectures)
+        if any(c.identifier.endswith(arch.value) for arch in architectures)
         and build_selector(c.identifier)
     ]
 
diff --git a/cibuildwheel/util.py b/cibuildwheel/util.py
index a2196b09..70eaa44d 100644
--- a/cibuildwheel/util.py
+++ b/cibuildwheel/util.py
@@ -123,7 +123,7 @@ class DependencyConstraints:
         return f'{self.__class__.__name__}{self.base_file_path!r})'
 
 
-class Architecture(str, Enum):
+class Architecture(Enum):
     # mac/linux archs
     x86_64 = 'x86_64'
     i686 = 'i686'
@@ -201,7 +201,7 @@ def strtobool(val: str) -> bool:
     return False
 
 
-class CIProvider(str, Enum):
+class CIProvider(Enum):
     travis_ci = 'travis'
     appveyor = 'appveyor'
     circle_ci = 'circle_ci'