Don't consider comparing True and False as a dangerous comparison (#9021)

Fixes #9011.

Author: JukkaL

mypy/checkexpr.py

@@ -2306,6 +2306,10 @@ def dangerous_comparison(self, left: Type, right: Type,
                 left = map_instance_to_supertype(left, abstract_set)
                 right = map_instance_to_supertype(right, abstract_set)
                 return not is_overlapping_types(left.args[0], right.args[0])
+        if isinstance(left, LiteralType) and isinstance(right, LiteralType):
+            if isinstance(left.value, bool) and isinstance(right.value, bool):
+                # Comparing different booleans is not dangerous.
+                return False
         return not is_overlapping_types(left, right, ignore_promotions=False)
 
     def get_operator_method(self, op: str) -> str:

test-data/unit/check-literal.test

@@ -3228,3 +3228,18 @@ y: Literal[F.A]
 reveal_type(x)  # N: Revealed type is 'Literal[__main__.Foo.A]'
 reveal_type(y)  # N: Revealed type is 'Literal[__main__.Foo.A]'
 [builtins fixtures/tuple.pyi]
+
+[case testStrictEqualityLiteralTrueVsFalse]
+# mypy: strict-equality
+
+class C:
+    a = True
+
+    def update(self) -> None:
+        self.a = False
+
+c = C()
+assert c.a is True
+c.update()
+assert c.a is False
+[builtins fixtures/bool.pyi]