The issue was that the object dtype is misleading. I thought it mean that all items were strings. But apparently, while reading the file pandas was converting some elements to ints, and leaving the remainders as strings.
The solution was to make sure that every field is a string:
>>> df1.col1 = df1.col1.astype(str)
>>> df2.col2 = df2.col2.astype(str)
Then the merge works as expected.
(I wish there was a way of specifying a dtype of str…)