pandas isin() fail between dataframes with objects types columns

The pd.DataFrame.isin docs spell out this behavior pretty clearly, emphasis my own.

If values is a DataFrame, then both the index and column labels must match.

So looking at your two DataFrames side by side:

a   isin  pd.DataFrame([1,'a'])

   0           0
0  1        0  1    True  <- 1 == 1 for col label (0) and index label (0) 
1  2        1  a    False <- 2 != 'a' for col label (0) and index label (1)
2  a                False <- Nothing to align