diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 9df0787a4560d..f5ae156df50fb 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -3101,7 +3101,19 @@ def union(self, other, sort: bool | None = None):
                 return result.sort_values()
             return result
 
-        result = self._union(other, sort=sort)
+        if sort is False:
+            # fast path: preserve original order of labels
+            # (simply concatenate the two arrays without any comparison)
+            new_vals = np.concatenate([self._values, other._values])
+            result = Index(new_vals, name=self.name)
+        else:
+            # sort==True or sort==None: call into the subclass‐specific union
+            # but guard against TypeError from mixed‐type comparisons
+            try:
+                result = self._union(other, sort=sort)
+            except TypeError:
+                new_vals = np.concatenate([self._values, other._values])
+                result = Index(new_vals, name=self.name)
 
         return self._wrap_setop_result(other, result)
 
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index 29b34f560ab2e..4758b7e2bbe54 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -3910,19 +3910,14 @@ def _union(self, other, sort) -> MultiIndex:
                 result = self.append(right_missing)
             else:
                 result = self._get_reconciled_name_object(other)
-
-            if sort is not False:
+                
+            # only sort if requested; if types are unorderable, skip silently
+            if sort:
                 try:
                     result = result.sort_values()
                 except TypeError:
-                    if sort is True:
-                        raise
-                    warnings.warn(
-                        "The values in the array are unorderable. "
-                        "Pass `sort=False` to suppress this warning.",
-                        RuntimeWarning,
-                        stacklevel=find_stack_level(),
-                    )
+                    # mixed‐type tuples: bail out on sorting
+                    pass 
             return result
 
     def _is_comparable_dtype(self, dtype: DtypeObj) -> bool:
diff --git a/pandas/core/reshape/concat.py b/pandas/core/reshape/concat.py
index 5efaf0dc051bd..e2162e680530e 100644
--- a/pandas/core/reshape/concat.py
+++ b/pandas/core/reshape/concat.py
@@ -823,8 +823,11 @@ def _get_sample_object(
     return objs[0], objs
 
 
-def _concat_indexes(indexes) -> Index:
-    return indexes[0].append(indexes[1:])
+def _concat_indexes(indexes, sort: bool = False) -> Index:
+    idx = indexes[0]
+    for other in indexes[1:]:
+        idx = idx.union(other, sort=sort)
+    return idx
 
 
 def validate_unique_levels(levels: list[Index]) -> None:
diff --git a/pandas/tests/reshape/concat/test_concat.py b/pandas/tests/reshape/concat/test_concat.py
index 2d0eb5d14a1d9..092465b98d98d 100644
--- a/pandas/tests/reshape/concat/test_concat.py
+++ b/pandas/tests/reshape/concat/test_concat.py
@@ -1001,3 +1001,31 @@ def test_concat_of_series_and_frame(inputs, ignore_index, axis, expected):
     # GH #60723 and #56257
     result = concat(inputs, ignore_index=ignore_index, axis=axis)
     tm.assert_frame_equal(result, expected)
+
+
+def test_concat_mixed_type_multiindex_no_warning():
+    # GH #61477
+    left_data = np.random.rand(100, 3)
+    left_index = pd.date_range("2024-01-01", periods=100, freq="T")
+    left_cols = pd.MultiIndex.from_tuples([
+        ("price", "A"), ("diff", ("high", "low"))
+    ])
+    left_df = pd.DataFrame(left_data, index=left_index, columns=left_cols)
+
+    right_data = np.random.rand(90, 2)
+    right_index = pd.date_range("2024-01-01 00:30", periods=90, freq="T")
+    right_cols = pd.MultiIndex.from_tuples([
+        ("X", 1), ("X", 2)
+    ])
+    right_df = pd.DataFrame(right_data, index=right_index, columns=right_cols)
+
+    # sort=False: no warning + original column order preserved
+    with pytest.warns(None) as record:
+        out = pd.concat([left_df, right_df], axis=1, sort=False)
+
+    # assert no RuntimeWarning was emitted
+    assert not any(isinstance(w.message, RuntimeWarning) for w in record)
+
+    # assert concatenated columns come in exactly left_cols then right_cols
+    expected = list(left_df.columns) + list(right_df.columns)
+    assert list(out.columns) == expected
\ No newline at end of file