diff --git a/xarray/core/duck_array_ops.py b/xarray/core/duck_array_ops.py
index e10ab5a3558..2d30fb41eaa 100644
--- a/xarray/core/duck_array_ops.py
+++ b/xarray/core/duck_array_ops.py
@@ -409,6 +409,13 @@ def where(condition, x, y):
     xp = get_array_namespace(condition, x, y)
 
     dtype = xp.bool_ if hasattr(xp, "bool_") else xp.bool
+    if isinstance(
+        condition, pd.api.extensions.ExtensionArray
+    ) and pd.api.types.is_bool_dtype(condition.dtype):
+        # pandas nullable booleans can contain <NA>, which cannot be cast
+        # directly to bool. For masking semantics, treat missing condition
+        # values as False.
+        condition = condition.fillna(False)
     if not is_duck_array(condition):
         condition = asarray(condition, dtype=dtype, xp=xp)
     else:
diff --git a/xarray/core/indexes.py b/xarray/core/indexes.py
index 2242e57e482..3488f65ce1b 100644
--- a/xarray/core/indexes.py
+++ b/xarray/core/indexes.py
@@ -914,7 +914,13 @@ def join(
             index = self.index.intersection(other.index)
         if is_allowed_extension_array_dtype(index.dtype):
             return type(self)(index, self.dim)
-        coord_dtype = np.result_type(self.coord_dtype, other.coord_dtype)
+        try:
+            coord_dtype = np.result_type(self.coord_dtype, other.coord_dtype)
+        except TypeError:
+            # pandas extension dtypes (e.g., CategoricalDtype) are not always
+            # compatible with numpy's type promotion even when the resulting
+            # index dtype is a regular NumPy dtype.
+            coord_dtype = get_valid_numpy_dtype(index)
         return type(self)(index, self.dim, coord_dtype=coord_dtype)
 
     def reindex_like(
diff --git a/xarray/tests/test_dataarray.py b/xarray/tests/test_dataarray.py
index 8eb52046a31..e5d791212f8 100644
--- a/xarray/tests/test_dataarray.py
+++ b/xarray/tests/test_dataarray.py
@@ -2006,6 +2006,42 @@ def test_dropna_extension_array(self, extension_array) -> None:
         assert filled.dtype == srs.dtype
         assert (filled.values == srs.values[1:]).all()
 
+    @pytest.mark.parametrize(
+        "dtype",
+        [
+            pytest.param("Int64", id="Int64"),
+            pytest.param("int64[pyarrow]", id="int64[pyarrow]", marks=requires_pyarrow),
+        ],
+    )
+    def test_where_nullable_int_no_float_promotion(self, dtype) -> None:
+        srs = pd.Series([1, 2, None], dtype=dtype, name="v")
+        da = srs.to_xarray()
+        actual = da.where(da > 1)
+
+        assert actual.dtype != np.dtype(np.float64)
+        assert_array_equal(actual.isnull(), [True, False, True])
+        assert actual.fillna(0).astype("int64").data.tolist() == [0, 2, 0]
+
+    @requires_pyarrow
+    def test_date32_pyarrow_coord_align(self) -> None:
+        dates = pd.date_range("2024-01-01", periods=3, freq="D")
+        date32_index = pd.Index(
+            pd.Series(dates, name="date").astype("date32[pyarrow]"), name="time"
+        )
+
+        da1 = xr.DataArray(
+            [10.0, 20.0, 30.0], dims="time", coords={"time": date32_index}
+        )
+        da2 = xr.DataArray(
+            [1.0, 2.0, 3.0],
+            dims="time",
+            coords={"time": pd.date_range("2024-01-01", periods=3, freq="D")},
+        )
+
+        actual1, actual2 = xr.align(da1, da2, join="outer")
+        assert actual1.sizes["time"] == 3
+        assert actual2.sizes["time"] == 3
+
     def test_rename(self) -> None:
         da = xr.DataArray(
             [1, 2, 3], dims="dim", name="name", coords={"coord": ("dim", [5, 6, 7])}
diff --git a/xarray/tests/test_indexes.py b/xarray/tests/test_indexes.py
index 94adcc3b935..e35be123598 100644
--- a/xarray/tests/test_indexes.py
+++ b/xarray/tests/test_indexes.py
@@ -280,6 +280,24 @@ def test_join(self) -> None:
         assert actual.equals(expected)
         assert actual.coord_dtype == "=U4"
 
+    def test_join_categorical_and_object(self) -> None:
+        index1 = PandasIndex(pd.Index(["A", "B"], dtype=object), "x")
+        index2 = PandasIndex(
+            pd.CategoricalIndex(["B", "C"], categories=["A", "B", "C"], name="x"),
+            "x",
+        )
+
+        expected = PandasIndex(pd.Index(["B"], dtype=object), "x")
+        actual = index1.join(index2)
+
+        assert actual.equals(expected)
+        assert actual.coord_dtype == np.dtype(object)
+
+        expected = PandasIndex(pd.Index(["A", "B", "C"], dtype=object), "x")
+        actual = index1.join(index2, how="outer")
+        assert actual.equals(expected)
+        assert actual.coord_dtype == np.dtype(object)
+
     def test_reindex_like(self) -> None:
         index1 = PandasIndex([0, 1, 2], "x")
         index2 = PandasIndex([1, 2, 3, 4], "x")