I'm a little confused here I think. When I write a new regression test that more closely matches the original reproducer, like below, it errors out here.

--- a/numpy/ma/tests/test_core.py
+++ b/numpy/ma/tests/test_core.py
@@ -1461,6 +1461,11 @@ def test_minmax_object_dtype(self, arg1, arg2, arg3):
         assert a.min() is arg1
         assert a.max() is arg3
 
+
+    def test_gh_9103(self):
+        arr = masked_array([1, 2, 3], dtype='object', mask=[True, False, False])
+        assert arr.min() == 2

_____________________________________________________________________________ TestMaskedArrayArithmetic.test_gh_9103 ______________________________________________________________________________

self = <numpy.ma.tests.test_core.TestMaskedArrayArithmetic object at 0x1033739b0>

    def test_gh_9103(self):
        arr = masked_array([1, 2, 3], dtype='object', mask=[True, False, False])
>       assert arr.min() == 2

arr        = masked_array(data=[--, 2, 3],
             mask=[ True, False, False],
       fill_value=np.str_('?'),
            dtype=object)
self       = <numpy.ma.tests.test_core.TestMaskedArrayArithmetic object at 0x1033739b0>

numpy/ma/tests/test_core.py:1467: 
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
numpy/ma/core.py:5944: in min
    result = self.filled(fill_value).min(
        _mask      = array([ True, False, False])
        axis       = None
        fill_value = None
        keepdims   = <no value>
        kwargs     = {}
        newmask    = np.False_
        out        = None
        self       = masked_array(data=[--, 2, 3],
             mask=[ True, False, False],
       fill_value=np.str_('?'),
            dtype=object)
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

a = array(['?', 2, 3], dtype=object), axis = None, out = None, keepdims = False, initial = <no value>, where = True

    def _amin(a, axis=None, out=None, keepdims=False,
              initial=_NoValue, where=True):
>       return umr_minimum(a, axis, None, out, keepdims, initial, where)
E       TypeError: '<=' not supported between instances of 'str' and 'int'

a          = array(['?', 2, 3], dtype=object)
axis       = None
initial    = <no value>
keepdims   = False
out        = None
where      = True

numpy/_core/_methods.py:45: TypeError

That's a great catch, I totally neglected to even test the masked array with an actual mask! I would say that is a separate bug from the one I'm trying to fix though. Actually it seems like it may be a regression that has occurred in the 8 years since #9103 was reported. Even without my change, in current versions of numpy, the #9103 reproducer now gives that TypeError rather than the AttributeError. Of course you can work around this by setting an appropriate fill_value other than '?' (and arguably you should have a fill_value that matches the actual data you're storing in the array). But I'm not sure why it worked at all in 2017. I'll look into it a bit more.

Hmm... even with the contemporary numpy 1.13.0 from 2017, I'm seeing the TypeError rather than the AttributeError on the #9103 reproducer. I only get the AttributeError if I remove the mask or set a fill_value. I'd test older versions, but I'm running into some segfaults.

I've been trying to think if there is any "good" way to fix the TypeError issue, besides the obvious way of creating a universal infinity object that compares greater to any other object regardless of type¹, and putting that in min_filler, but really I don't think there is (short of completely reimplementing min). That said, it should be a very easy fix to create such an object, so I'd be willing to add that to the PR if you think it is an acceptable solution.

There is an (extreme) edge case I am aware of here that my code fails to address: ideally, I think that

x = np.array([1, 2])
assert np.fromiter([x], dtype=object).view(np.ma.MaskedArray).min() is x

should pass, but with my change, x will get erroneously converted to a masked array when returned by min.

This is identical to the old behavior, so it's not necessarily a problem, but it is a failure of my assumptions: initially when working on this PR, I thought I only needed to worry about arrays containing 0-D array objects, since arrays of higher dimension are not orderable (and so you'd just get an error when calling min(), as you should). But of course I forgot to consider that min() will succeed regardless if there is only one item. Also, as another similar edge case, higher dimensional arrays actually are orderable if they themselves only contain one item (not just if they are 0-D).

I'm not sure if this is actually worth fixing though. Thoughts?