diff --git a/numpy/_core/strings.py b/numpy/_core/strings.py
index 8707bed2ffbb..db7852e1946a 100644
--- a/numpy/_core/strings.py
+++ b/numpy/_core/strings.py
@@ -235,6 +235,8 @@ def find(a, sub, start=0, end=None):
 
     """
     end = end if end is not None else MAX
+    a = np.asanyarray(a)
+    sub = np.asanyarray(sub, dtype=getattr(sub, "dtype", a.dtype))
     return _find_ufunc(a, sub, start, end)
 
 
@@ -265,6 +267,8 @@ def rfind(a, sub, start=0, end=None):
 
     """
     end = end if end is not None else MAX
+    a = np.asanyarray(a)
+    sub = np.asanyarray(sub, dtype=getattr(sub, "dtype", a.dtype))
     return _rfind_ufunc(a, sub, start, end)
 
 
@@ -277,6 +281,7 @@ def index(a, sub, start=0, end=None):
     a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
 
     sub : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        The substring to search for.
 
     start, end : array_like, with any integer dtype, optional
 
@@ -297,6 +302,8 @@ def index(a, sub, start=0, end=None):
 
     """
     end = end if end is not None else MAX
+    a = np.asanyarray(a)
+    sub = np.asanyarray(sub, dtype=getattr(sub, "dtype", a.dtype))
     return _index_ufunc(a, sub, start, end)
 
 
@@ -307,9 +314,10 @@ def rindex(a, sub, start=0, end=None):
 
     Parameters
     ----------
-    a : array-like, with `np.bytes_` or `np.str_` dtype
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
 
-    sub : array-like, with `np.bytes_` or `np.str_` dtype
+    sub : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        The substring to search for.
 
     start, end : array-like, with any integer dtype, optional
 
@@ -327,9 +335,11 @@ def rindex(a, sub, start=0, end=None):
     >>> a = np.array(["Computer Science"])
     >>> np.strings.rindex(a, "Science", start=0, end=None)
     array([9])
-    
+
     """
     end = end if end is not None else MAX
+    a = np.asanyarray(a)
+    sub = np.asanyarray(sub, dtype=getattr(sub, "dtype", a.dtype))
     return _rindex_ufunc(a, sub, start, end)
 
 
@@ -373,6 +383,8 @@ def count(a, sub, start=0, end=None):
 
     """
     end = end if end is not None else MAX
+    a = np.asanyarray(a)
+    sub = np.asanyarray(sub, dtype=getattr(sub, "dtype", a.dtype))
     return _count_ufunc(a, sub, start, end)
 
 
@@ -386,6 +398,7 @@ def startswith(a, prefix, start=0, end=None):
     a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
 
     prefix : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        The substring to search for.
 
     start, end : array_like, with any integer dtype
         With ``start``, test beginning at that position. With ``end``,
@@ -402,6 +415,8 @@ def startswith(a, prefix, start=0, end=None):
 
     """
     end = end if end is not None else MAX
+    a = np.asanyarray(a)
+    prefix = np.asanyarray(prefix, dtype=getattr(prefix, "dtype", a.dtype))
     return _startswith_ufunc(a, prefix, start, end)
 
 
@@ -415,6 +430,7 @@ def endswith(a, suffix, start=0, end=None):
     a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
 
     suffix : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        The substring to search for.
 
     start, end : array_like, with any integer dtype
         With ``start``, test beginning at that position. With ``end``,
@@ -441,6 +457,8 @@ def endswith(a, suffix, start=0, end=None):
 
     """
     end = end if end is not None else MAX
+    a = np.asanyarray(a)
+    suffix = np.asanyarray(suffix, dtype=getattr(suffix, "dtype", a.dtype))
     return _endswith_ufunc(a, suffix, start, end)
 
 
@@ -595,7 +613,9 @@ def center(a, width, fillchar=' '):
     width : array_like, with any integer dtype
         The length of the resulting strings, unless ``width < str_len(a)``.
     fillchar : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
-        Optional padding character to use (default is space).
+        Optional padding character to use (default is space). If ``a`` and
+        ``fillchar`` have fixed-width dtypes, then ``fillchar`` will be
+        truncated to the length of ``a``.
 
     Returns
     -------
@@ -627,7 +647,7 @@ def center(a, width, fillchar=' '):
     """
     a = np.asanyarray(a)
     width = np.maximum(str_len(a), width)
-    fillchar = np.asanyarray(fillchar, dtype=a.dtype)
+    fillchar = np.asanyarray(fillchar, a.dtype)
 
     if np.any(str_len(fillchar) != 1):
         raise TypeError(
@@ -654,7 +674,9 @@ def ljust(a, width, fillchar=' '):
     width : array_like, with any integer dtype
         The length of the resulting strings, unless ``width < str_len(a)``.
     fillchar : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
-        Optional character to use for padding (default is space).
+        Optional character to use for padding (default is space). If ``a`` and
+        ``fillchar`` have fixed-width dtypes, then ``fillchar`` will be
+        truncated to the length of ``a``.
 
     Returns
     -------
@@ -683,7 +705,7 @@ def ljust(a, width, fillchar=' '):
     """
     a = np.asanyarray(a)
     width = np.maximum(str_len(a), width)
-    fillchar = np.asanyarray(fillchar, dtype=a.dtype)
+    fillchar = np.asanyarray(fillchar, a.dtype)
 
     if np.any(str_len(fillchar) != 1):
         raise TypeError(
@@ -710,7 +732,9 @@ def rjust(a, width, fillchar=' '):
     width : array_like, with any integer dtype
         The length of the resulting strings, unless ``width < str_len(a)``.
     fillchar : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
-        Optional padding character to use (default is space).
+        Optional padding character to use (default is space). If ``a`` and
+        ``fillchar`` have fixed-width dtypes, then ``fillchar`` will be
+        truncated to the length of ``a``.
 
     Returns
     -------
@@ -739,7 +763,7 @@ def rjust(a, width, fillchar=' '):
     """
     a = np.asanyarray(a)
     width = np.maximum(str_len(a), width)
-    fillchar = np.asanyarray(fillchar, dtype=a.dtype)
+    fillchar = np.asanyarray(fillchar, a.dtype)
 
     if np.any(str_len(fillchar) != 1):
         raise TypeError(
@@ -838,7 +862,9 @@ def lstrip(a, chars=None):
     """
     if chars is None:
         return _lstrip_whitespace(a)
-    return _lstrip_chars(a, chars)
+    a = np.asanyarray(a)
+    return _lstrip_chars(
+        a, np.asanyarray(chars, getattr(chars, "dtype", a.dtype)))
 
 
 def rstrip(a, chars=None):
@@ -879,7 +905,9 @@ def rstrip(a, chars=None):
     """
     if chars is None:
         return _rstrip_whitespace(a)
-    return _rstrip_chars(a, chars)
+    a = np.asanyarray(a)
+    return _rstrip_chars(
+        a, np.asanyarray(chars, getattr(chars, "dtype", a.dtype)))
 
 
 def strip(a, chars=None):
@@ -924,7 +952,9 @@ def strip(a, chars=None):
     """
     if chars is None:
         return _strip_whitespace(a)
-    return _strip_chars(a, chars)
+    a = np.asanyarray(a)
+    return _strip_chars(
+        a, np.asanyarray(chars, getattr(chars, "dtype", a.dtype)))
 
 
 def upper(a):
@@ -1120,9 +1150,9 @@ def replace(a, old, new, count=-1):
 
     Parameters
     ----------
-    a : array_like, with ``bytes_`` or ``str_`` dtype
+    a : array_like, with ``StringDType``, ``bytes_`` or ``str_`` dtype
 
-    old, new : array_like, with ``bytes_`` or ``str_`` dtype
+    old, new : array_like, with ``StringDType``, ``bytes_`` or ``str_`` dtype
 
     count : array_like, with ``int_`` dtype
         If the optional argument ``count`` is given, only the first
@@ -1147,7 +1177,7 @@ def replace(a, old, new, count=-1):
     >>> a = np.array(["The dish is fresh", "This is it"])
     >>> np.strings.replace(a, 'is', 'was')
     array(['The dwash was fresh', 'Thwas was it'], dtype='<U19')
-    
+
     """
     arr = np.asanyarray(a)
     a_dt = arr.dtype
@@ -1361,8 +1391,7 @@ def partition(a, sep):
 
     """
     a = np.asanyarray(a)
-    # TODO switch to copy=False when issues around views are fixed
-    sep = np.array(sep, dtype=a.dtype, copy=True, subok=True)
+    sep = np.asanyarray(sep, dtype=getattr(sep, "dtype", a.dtype))
     if a.dtype.char == "T":
         return _partition(a, sep)
 
@@ -1426,8 +1455,7 @@ def rpartition(a, sep):
 
     """
     a = np.asanyarray(a)
-    # TODO switch to copy=False when issues around views are fixed
-    sep = np.array(sep, dtype=a.dtype, copy=True, subok=True)
+    sep = np.asanyarray(sep, dtype=getattr(sep, "dtype", a.dtype))
     if a.dtype.char == "T":
         return _rpartition(a, sep)
 
diff --git a/numpy/_core/tests/test_stringdtype.py b/numpy/_core/tests/test_stringdtype.py
index 378d1886d26a..f57842a3f2db 100644
--- a/numpy/_core/tests/test_stringdtype.py
+++ b/numpy/_core/tests/test_stringdtype.py
@@ -1193,6 +1193,22 @@ def test_unary(string_array, unicode_array, function_name):
     NULLS_ALWAYS_ERROR
 )
 
+STRING_SECOND_ARGUMENT = [
+    "find",
+    "rfind",
+    "index",
+    "rindex",
+    "count",
+    "startswith",
+    "endswith",
+    "lstrip",
+    "rstrip",
+    "strip",
+    "partition",
+    "rpartition",
+    "replace",
+]
+
 
 def call_func(func, args, array, sanitize=True):
     if args == (None, None):
@@ -1221,6 +1237,14 @@ def test_binary(string_array, unicode_array, function_name, args):
         ures = ures.astype(StringDType())
     assert_array_equal(sres, ures)
 
+    if function_name in STRING_SECOND_ARGUMENT:
+        # call again with a non-default stringdtype instance, this should
+        # work even though the inferred dtype for the second argument is
+        # the default stringdtype instance
+        sres = call_func(func, args,
+                         string_array.astype(StringDType(na_object="foobar")))
+        assert_array_equal(sres, ures)
+
     dtype = string_array.dtype
     if function_name not in SUPPORTS_NULLS or not hasattr(dtype, "na_object"):
         return