diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 5c04678cd5fa6..58494d2fcaa5f 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -7995,35 +7995,44 @@ def blk_func(values):
                 out[:] = coerce_to_dtypes(out.values, df.dtypes)
             return out
 
+        if not self._is_homogeneous_type:
+            # try to avoid self.values call
+
+            if filter_type is None and axis == 0 and len(self) > 0:
+                # operate column-wise
+
+                # numeric_only must be None here, as other cases caught above
+                # require len(self) > 0 bc frame_apply messes up empty prod/sum
+
+                # this can end up with a non-reduction
+                # but not always. if the types are mixed
+                # with datelike then need to make sure a series
+
+                # we only end up here if we have not specified
+                # numeric_only and yet we have tried a
+                # column-by-column reduction, where we have mixed type.
+                # So let's just do what we can
+                from pandas.core.apply import frame_apply
+
+                opa = frame_apply(
+                    self, func=f, result_type="expand", ignore_failures=True
+                )
+                result = opa.get_result()
+                if result.ndim == self.ndim:
+                    result = result.iloc[0].rename(None)
+                return result
+
+        data = self
         if numeric_only is None:
             data = self
             values = data.values
+
             try:
                 result = f(values)
 
             except TypeError:
                 # e.g. in nanops trying to convert strs to float
 
-                # try by-column first
-                if filter_type is None and axis == 0:
-                    # this can end up with a non-reduction
-                    # but not always. if the types are mixed
-                    # with datelike then need to make sure a series
-
-                    # we only end up here if we have not specified
-                    # numeric_only and yet we have tried a
-                    # column-by-column reduction, where we have mixed type.
-                    # So let's just do what we can
-                    from pandas.core.apply import frame_apply
-
-                    opa = frame_apply(
-                        self, func=f, result_type="expand", ignore_failures=True
-                    )
-                    result = opa.get_result()
-                    if result.ndim == self.ndim:
-                        result = result.iloc[0]
-                    return result
-
                 # TODO: why doesnt axis matter here?
                 data = _get_data(axis_matters=False)
                 labels = data._get_agg_axis(axis)
@@ -8031,6 +8040,7 @@ def blk_func(values):
                 values = data.values
                 with np.errstate(all="ignore"):
                     result = f(values)
+
         else:
             if numeric_only:
                 data = _get_data(axis_matters=True)
diff --git a/pandas/tests/frame/test_analytics.py b/pandas/tests/frame/test_analytics.py
index 3a7df29ae9091..6525e93d89fce 100644
--- a/pandas/tests/frame/test_analytics.py
+++ b/pandas/tests/frame/test_analytics.py
@@ -346,7 +346,9 @@ def kurt(x):
             "sum", np.sum, float_frame_with_na, skipna_alternative=np.nansum
         )
         assert_stat_op_calc("mean", np.mean, float_frame_with_na, check_dates=True)
-        assert_stat_op_calc("product", np.prod, float_frame_with_na)
+        assert_stat_op_calc(
+            "product", np.prod, float_frame_with_na, skipna_alternative=np.nanprod
+        )
 
         assert_stat_op_calc("mad", mad, float_frame_with_na)
         assert_stat_op_calc("var", var, float_frame_with_na)
diff --git a/pandas/tests/frame/test_missing.py b/pandas/tests/frame/test_missing.py
index e4de749c5f5c5..7cb7115276f71 100644
--- a/pandas/tests/frame/test_missing.py
+++ b/pandas/tests/frame/test_missing.py
@@ -372,8 +372,12 @@ def test_fillna_categorical_nan(self):
         cat = Categorical([np.nan, 2, np.nan])
         val = Categorical([np.nan, np.nan, np.nan])
         df = DataFrame({"cats": cat, "vals": val})
-        with tm.assert_produces_warning(RuntimeWarning):
-            res = df.fillna(df.median())
+
+        # GH#32950 df.median() is poorly behaved because there is no
+        #  Categorical.median
+        median = Series({"cats": 2.0, "vals": np.nan})
+
+        res = df.fillna(median)
         v_exp = [np.nan, np.nan, np.nan]
         df_exp = DataFrame({"cats": [2, 2, 2], "vals": v_exp}, dtype="category")
         tm.assert_frame_equal(res, df_exp)