In what context is this a problem? A numpy object array of str objects is very string like [he says having flash-backs to MATLAB days].

I use seaborn, and a pandas.Dataframe to scatter some points.
Here, I need to concatenate a label vector (of type object) to my data matrix. Such operation causes the DataFrame to force all columns to have the object type.

For the moment, in my project, I overcame the issue by forcing the columns related to the points to have again the float type, since the is_string_like function with object arrays seems to consider my columns as strings.

I understand this may be an unexpected behaviour of numpy, rather than matplotlib's.
In fact, the operation

np.array(['1','2'], dtype=object) + ''

does not generate any type of errors or warnings. It simply has no effect.
Regarding the observations, I'd say that

np.array(['1','2'], dtype=str) + ''

instead, generates an error, hence is_string_like in this case would return False.

It seemed reasonable, however, to open an issue here, due to the fact that assuming the generation of some errors in such operations, causes the function to consider strings something which is not.

That sounds like pandas is doing something wrong (as one of the big advantages of panadas over numpy is to have heterogeneous columns)

That test has no effect because you are adding an empty string, if you do

In [5]: np.array(['1','2'], dtype=object) + 'b'
Out[5]: 
array(['1b', '2b'], dtype=object)

what is doing is clearer (the add unfunc is falling back to defering to python to deal with the + operation and giving you back a new object array with concatenation broadcast across all entries).

In the second case, you get

In [4]: np.array(['1','2'], dtype=str) + ''
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-4-1ccaacc2525d> in <module>()
----> 1 np.array(['1','2'], dtype=str) + ''

TypeError: ufunc 'add' did not contain a loop with signature matching types dtype('<U1') dtype('<U1') dtype('<U1')

Because instead of holding the values as python string objects (which know how to add with another string and is just a black-box to numpy) it is holding the values as fixed length c-strings and the dispatch mechanism in numpy does not know how to deal with this.