BUG: make is_string_dtype stricter

Resolves pandas-dev#15585.

Author: alexreg

pandas/core/dtypes/common.py

@@ -15,6 +15,7 @@
     Interval,
     Period,
     algos,
+    lib,
 )
 from pandas._libs.tslibs import conversion
 from pandas._typing import (
@@ -558,8 +559,12 @@ def is_string_dtype(arr_or_dtype) -> bool:
     >>> is_string_dtype(pd.Series([1, 2]))
     False
     """
-    # TODO: gh-15585: consider making the checks stricter.
+
     def condition(dtype) -> bool:
+        if isinstance(arr_or_dtype, np.ndarray):
+            if not lib.infer_dtype(arr_or_dtype) in ("string", "unicode"):
+                return False
+
         return dtype.kind in ("O", "S", "U") and not is_excluded_dtype(dtype)
 
     def is_excluded_dtype(dtype) -> bool:
@@ -1316,7 +1321,6 @@ def is_bool_dtype(arr_or_dtype) -> bool:
         # now we use the special definition for Index
 
     if isinstance(arr_or_dtype, ABCIndex):
-
         # TODO(jreback)
         # we don't have a boolean Index class
         # so its object, we need to infer to
@@ -1666,7 +1670,6 @@ def infer_dtype_from_object(dtype) -> DtypeObj:
     if is_extension_array_dtype(dtype):
         return dtype.type
     elif isinstance(dtype, str):
-
         # TODO(jreback)
         # should deprecate these
         if dtype in ["datetimetz", "datetime64tz"]: