diff --git a/pandas/core/dtypes/common.py b/pandas/core/dtypes/common.py
index 99415b6fc6ec8..5dbfa21715842 100644
--- a/pandas/core/dtypes/common.py
+++ b/pandas/core/dtypes/common.py
@@ -635,6 +635,18 @@ def is_string_dtype(arr_or_dtype) -> bool:
     >>> is_string_dtype(pd.Series([1, 2], dtype=object))
     False
     """
+    # Handle Categorical consistently whether passed as array or dtype
+    if hasattr(arr_or_dtype, "dtype") and isinstance(
+        _get_dtype(arr_or_dtype), CategoricalDtype
+    ):
+        return is_all_strings(arr_or_dtype)
+    elif isinstance(arr_or_dtype, CategoricalDtype):
+        # For CategoricalDtype, check if categories are strings
+        # Handle case where categories is None
+        if arr_or_dtype.categories is None:
+            return False
+        return arr_or_dtype.categories.inferred_type == "string"
+
     if hasattr(arr_or_dtype, "dtype") and _get_dtype(arr_or_dtype).kind == "O":
         return is_all_strings(arr_or_dtype)
 
@@ -1900,6 +1912,9 @@ def is_all_strings(value: ArrayLike) -> bool:
                 np.asarray(value), skipna=False
             )
     elif isinstance(dtype, CategoricalDtype):
+        # Handle case where categories is None
+        if dtype.categories is None:
+            return False
         return dtype.categories.inferred_type == "string"
     return dtype == "string"
 
diff --git a/pandas/core/indexes/datetimelike.py b/pandas/core/indexes/datetimelike.py
index 62831f941b535..2af351b66cf5d 100644
--- a/pandas/core/indexes/datetimelike.py
+++ b/pandas/core/indexes/datetimelike.py
@@ -180,7 +180,11 @@ def equals(self, other: Any) -> bool:
                 should_try = other.inferred_type in inferable
             elif isinstance(other.dtype, CategoricalDtype):
                 other = cast("CategoricalIndex", other)
-                should_try = other.categories.inferred_type in inferable
+                # Handle case where categories is None
+                if other.categories is not None:
+                    should_try = other.categories.inferred_type in inferable
+                else:
+                    should_try = False
 
             if should_try:
                 try:
diff --git a/pandas/tests/dtypes/test_common.py b/pandas/tests/dtypes/test_common.py
index cd5050cab8ad5..d69f810b92860 100644
--- a/pandas/tests/dtypes/test_common.py
+++ b/pandas/tests/dtypes/test_common.py
@@ -337,6 +337,23 @@ def test_is_string_dtype_nullable(nullable_string_dtype):
     assert com.is_string_dtype(pd.array(["a", "b"], dtype=nullable_string_dtype))
 
 
+def test_is_string_dtype_categorical():
+    # GH#XXXXX - is_string_dtype should be consistent for Categorical series and dtype
+    cat_series = pd.Categorical(["A", "B", "C"])
+    assert not com.is_string_dtype(cat_series)
+    assert not com.is_string_dtype(cat_series.dtype)
+
+    # Test with string categories
+    cat_string_series = pd.Categorical(["A", "B", "C"], categories=["A", "B", "C"])
+    assert com.is_string_dtype(cat_string_series)
+    assert com.is_string_dtype(cat_string_series.dtype)
+
+    # Test with non-string categories
+    cat_int_series = pd.Categorical([1, 2, 3], categories=[1, 2, 3])
+    assert not com.is_string_dtype(cat_int_series)
+    assert not com.is_string_dtype(cat_int_series.dtype)
+
+
 integer_dtypes: list = []
 
 
diff --git a/pandas/tests/frame/test_query_eval.py b/pandas/tests/frame/test_query_eval.py
index f93105498ac79..b599be5d042fe 100644
--- a/pandas/tests/frame/test_query_eval.py
+++ b/pandas/tests/frame/test_query_eval.py
@@ -168,7 +168,7 @@ def test_query_duplicate_column_name(self, engine, parser):
             }
         ).rename(columns={"B": "A"})
 
-        res = df.query('C == 1', engine=engine, parser=parser)
+        res = df.query("C == 1", engine=engine, parser=parser)
 
         expect = DataFrame(
             [[1, 1, 1]],
@@ -1411,7 +1411,7 @@ def test_expr_with_column_name_with_backtick_and_hash(self):
     def test_expr_with_column_name_with_backtick(self):
         # GH 59285
         df = DataFrame({"a`b": (1, 2, 3), "ab": (4, 5, 6)})
-        result = df.query("`a``b` < 2")  # noqa
+        result = df.query("`a``b` < 2")
         # Note: Formatting checks may wrongly consider the above ``inline code``.
         expected = df[df["a`b"] < 2]
         tm.assert_frame_equal(result, expected)