diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index 2fe289a5f7c35..5c54753ce3666 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -710,6 +710,7 @@ ExtensionArray
 - Bug in :func:`array` failing to preserve :class:`PandasArray` (:issue:`43887`)
 - NumPy ufuncs ``np.abs``, ``np.positive``, ``np.negative`` now correctly preserve dtype when called on ExtensionArrays that implement ``__abs__, __pos__, __neg__``, respectively. In particular this is fixed for :class:`TimedeltaArray` (:issue:`43899`)
 - Avoid raising ``PerformanceWarning`` about fragmented DataFrame when using many columns with an extension dtype (:issue:`44098`)
+- Bug in :meth:`BooleanArray.__eq__` and :meth:`BooleanArray.__ne__` raising ``TypeError`` on comparison with an incompatible type (like a string). This caused :meth:`DataFrame.replace` to sometimes raise a ``TypeError`` if a nullable boolean column was included (:issue:`44499`)
 -
 
 Styler
diff --git a/pandas/core/arrays/boolean.py b/pandas/core/arrays/boolean.py
index 58e7abbbe1ddd..0787ec56379b2 100644
--- a/pandas/core/arrays/boolean.py
+++ b/pandas/core/arrays/boolean.py
@@ -44,6 +44,7 @@
     BaseMaskedArray,
     BaseMaskedDtype,
 )
+from pandas.core.ops import invalid_comparison
 
 if TYPE_CHECKING:
     import pyarrow
@@ -653,7 +654,11 @@ def _cmp_method(self, other, op):
             with warnings.catch_warnings():
                 warnings.filterwarnings("ignore", "elementwise", FutureWarning)
                 with np.errstate(all="ignore"):
-                    result = op(self._data, other)
+                    method = getattr(self._data, f"__{op.__name__}__")
+                    result = method(other)
+
+                if result is NotImplemented:
+                    result = invalid_comparison(self._data, other, op)
 
             # nans propagate
             if mask is None:
diff --git a/pandas/tests/arrays/boolean/test_logical.py b/pandas/tests/arrays/boolean/test_logical.py
index afcbe36e165c9..938fa8f1a5d6a 100644
--- a/pandas/tests/arrays/boolean/test_logical.py
+++ b/pandas/tests/arrays/boolean/test_logical.py
@@ -41,6 +41,20 @@ def test_empty_ok(self, all_logical_operators):
         result = getattr(a, op_name)(pd.NA)
         tm.assert_extension_array_equal(a, result)
 
+    @pytest.mark.parametrize(
+        "other", ["a", pd.Timestamp(2017, 1, 1, 12), np.timedelta64(4)]
+    )
+    def test_eq_mismatched_type(self, other):
+        # GH-44499
+        arr = pd.array([True, False])
+        result = arr == other
+        expected = pd.array([False, False])
+        tm.assert_extension_array_equal(result, expected)
+
+        result = arr != other
+        expected = pd.array([True, True])
+        tm.assert_extension_array_equal(result, expected)
+
     def test_logical_length_mismatch_raises(self, all_logical_operators):
         op_name = all_logical_operators
         a = pd.array([True, False, None], dtype="boolean")
diff --git a/pandas/tests/frame/methods/test_replace.py b/pandas/tests/frame/methods/test_replace.py
index 53b71bb489ebb..d6ecdcd155295 100644
--- a/pandas/tests/frame/methods/test_replace.py
+++ b/pandas/tests/frame/methods/test_replace.py
@@ -624,6 +624,15 @@ def test_replace_mixed3(self):
         expected.iloc[1, 1] = m[1]
         tm.assert_frame_equal(result, expected)
 
+    @pytest.mark.parametrize("dtype", ["boolean", "Int64", "Float64"])
+    def test_replace_with_nullable_column(self, dtype):
+        # GH-44499
+        nullable_ser = Series([1, 0, 1], dtype=dtype)
+        df = DataFrame({"A": ["A", "B", "x"], "B": nullable_ser})
+        result = df.replace("x", "X")
+        expected = DataFrame({"A": ["A", "B", "X"], "B": nullable_ser})
+        tm.assert_frame_equal(result, expected)
+
     def test_replace_simple_nested_dict(self):
         df = DataFrame({"col": range(1, 5)})
         expected = DataFrame({"col": ["a", 2, 3, "b"]})