BUG: merge not raising for String and numeric merges

doc/source/whatsnew/v2.2.0.rst

@@ -671,6 +671,7 @@ Reshaping
 - Bug in :func:`merge_asof` raising ``TypeError`` when ``by`` dtype is not ``object``, ``int64``, or ``uint64`` (:issue:`22794`)
 - Bug in :func:`merge_asof` raising incorrect error for string dtype (:issue:`56444`)
 - Bug in :func:`merge_asof` when using a :class:`Timedelta` tolerance on a :class:`ArrowDtype` column (:issue:`56486`)
+- Bug in :func:`merge` not raising when merging string columns with numeric columns (:issue:`56441`)
 - Bug in :func:`merge` returning columns in incorrect order when left and/or right is empty (:issue:`51929`)
 - Bug in :meth:`DataFrame.melt` where an exception was raised if ``var_name`` was not a string (:issue:`55948`)
 - Bug in :meth:`DataFrame.melt` where it would not preserve the datetime (:issue:`55254`)

pandas/core/reshape/merge.py

@@ -1354,8 +1354,12 @@ def _maybe_coerce_merge_keys(self) -> None:
 
             lk_is_cat = isinstance(lk.dtype, CategoricalDtype)
             rk_is_cat = isinstance(rk.dtype, CategoricalDtype)
-            lk_is_object = is_object_dtype(lk.dtype)
-            rk_is_object = is_object_dtype(rk.dtype)
+            lk_is_object_or_string = is_object_dtype(lk.dtype) or is_string_dtype(
+                lk.dtype
+            )
+            rk_is_object_or_string = is_object_dtype(rk.dtype) or is_string_dtype(
+                rk.dtype
+            )
 
             # if either left or right is a categorical
             # then the must match exactly in categories & ordered
@@ -1452,14 +1456,14 @@ def _maybe_coerce_merge_keys(self) -> None:
             # incompatible dtypes GH 9780, GH 15800
 
             # bool values are coerced to object
-            elif (lk_is_object and is_bool_dtype(rk.dtype)) or (
-                is_bool_dtype(lk.dtype) and rk_is_object
+            elif (lk_is_object_or_string and is_bool_dtype(rk.dtype)) or (
+                is_bool_dtype(lk.dtype) and rk_is_object_or_string
             ):
                 pass
 
             # object values are allowed to be merged
-            elif (lk_is_object and is_numeric_dtype(rk.dtype)) or (
-                is_numeric_dtype(lk.dtype) and rk_is_object
+            elif (lk_is_object_or_string and is_numeric_dtype(rk.dtype)) or (
+                is_numeric_dtype(lk.dtype) and rk_is_object_or_string
             ):
                 inferred_left = lib.infer_dtype(lk, skipna=False)
                 inferred_right = lib.infer_dtype(rk, skipna=False)
@@ -1498,7 +1502,7 @@ def _maybe_coerce_merge_keys(self) -> None:
                 # allows datetime with different resolutions
                 continue
 
-            elif lk_is_object and rk_is_object:
+            elif is_object_dtype(lk.dtype) and is_object_dtype(rk.dtype):
                 continue
 
             # Houston, we have a problem!

pandas/tests/reshape/merge/test_join.py

@@ -3,6 +3,8 @@
 import numpy as np
 import pytest
 
+import pandas.util._test_decorators as td
+
 import pandas as pd
 from pandas import (
     Categorical,
@@ -118,7 +120,10 @@ def test_handle_overlap_arbitrary_key(self, df, df2):
         assert "key1.foo" in joined
         assert "key2.bar" in joined
 
-    def test_join_on(self, target_source):
+    @pytest.mark.parametrize(
+        "infer_string", [False, pytest.param(True, marks=td.skip_if_no("pyarrow"))]
+    )
+    def test_join_on(self, target_source, infer_string):
         target, source = target_source
 
         merged = target.join(source, on="C")
@@ -150,8 +155,8 @@ def test_join_on(self, target_source):
         # overlap
         source_copy = source.copy()
         msg = (
-            "You are trying to merge on float64 and object columns for key 'A'. "
-            "If you wish to proceed you should use pd.concat"
+            "You are trying to merge on float64 and object|string columns for key "
+            "'A'. If you wish to proceed you should use pd.concat"
         )
         with pytest.raises(ValueError, match=msg):
             target.join(source_copy, on="A")