diff --git a/refurb/checks/readability/use_isinstance_bool.py b/refurb/checks/readability/use_isinstance_bool.py
index c557d8a..69b1714 100644
--- a/refurb/checks/readability/use_isinstance_bool.py
+++ b/refurb/checks/readability/use_isinstance_bool.py
@@ -71,10 +71,11 @@ def check(node: ComparisonExpr | OpExpr, errors: list[Error]) -> None:
         case OpExpr():
             match extract_binary_oper("or", node):
                 case (
-                    ComparisonExpr(operands=[lhs, t], operators=["is"]),
-                    ComparisonExpr(operands=[rhs, f], operators=["is"]),
+                    ComparisonExpr(operands=[lhs, t], operators=["is" | "==" as lhs_op]),
+                    ComparisonExpr(operands=[rhs, f], operators=["is" | "==" as rhs_op]),
                 ) if (
-                    is_equivalent(lhs, rhs)
+                    lhs_op == rhs_op
+                    and is_equivalent(lhs, rhs)
                     and ((is_true(t) and is_false(f)) or (is_false(t) and is_true(f)))
                 ):
                     old = stringify(node)
diff --git a/test/data/err_191.py b/test/data/err_191.py
index c8aa3b2..0655a0c 100644
--- a/test/data/err_191.py
+++ b/test/data/err_191.py
@@ -30,6 +30,9 @@
 _ = b is True or b is False  # noqa: FURB149
 _ = b is False or b is True  # noqa: FURB149
 
+_ = b == True or b == False  # noqa: FURB149, FURB108
+_ = b == False or b == True  # noqa: FURB149, FURB108
+
 
 # these should not
 if b in {True}: pass  # noqa: FURB171
@@ -68,5 +71,5 @@
 _ = b is False or b is not True  # noqa: FURB149
 
 # TODO: support this later
-_ = x is not True and x is not False  # noqa: FURB149
-_ = x is not False and x is not True  # noqa: FURB149
+_ = b is not True and b is not False  # noqa: FURB149
+_ = b is not False and b is not True  # noqa: FURB149
diff --git a/test/data/err_191.txt b/test/data/err_191.txt
index 9d30e2b..db54013 100644
--- a/test/data/err_191.txt
+++ b/test/data/err_191.txt
@@ -15,3 +15,5 @@ test/data/err_191.py:26:8 [FURB191]: Replace `b in {True, False}` with `isinstan
 test/data/err_191.py:28:4 [FURB191]: Replace `b not in {True, False}` with `not isinstance(b, bool)`
 test/data/err_191.py:30:5 [FURB191]: Replace `b is True or b is False` with `isinstance(b, bool)`
 test/data/err_191.py:31:5 [FURB191]: Replace `b is False or b is True` with `isinstance(b, bool)`
+test/data/err_191.py:33:5 [FURB191]: Replace `b == True or b == False` with `isinstance(b, bool)`
+test/data/err_191.py:34:5 [FURB191]: Replace `b == False or b == True` with `isinstance(b, bool)`