Setup
Borrowed @MaxU's df

df = pd.DataFrame([
    [1, 2, 3],
    [4, None, 6],
    [None, 7, 8],
    [9, 10, 11]
], dtype=object)

Solution
You can just use pd.DataFrame.dropna as is

df.dropna()

   0   1   2
0  1   2   3
3  9  10  11

Supposing you have None strings like in this df

df = pd.DataFrame([
    [1, 2, 3],
    [4, 'None', 6],
    ['None', 7, 8],
    [9, 10, 11]
], dtype=object)

Then combine dropna with mask

df.mask(df.eq('None')).dropna()

   0   1   2
0  1   2   3
3  9  10  11

You can ensure that the entire dataframe is object when you compare with.

df.mask(df.astype(object).eq('None')).dropna()

   0   1   2
0  1   2   3
3  9  10  11

You can nest list comprehensions:

df['Mar'] = [[x for x in inner_list if x is not None] for inner_list in df['Mar']]

You can also use filter to filter out None values

df['Mar'] = [list(filter(lambda x: x is None, inner_list)) for inner_list in df['Mar']]

You can use sorted, boolean indexing and fillna to do that.

pm = pivot_df.apply(sorted,key=pd.isnull)
new = pm[~pd.isnull(pm).all(1)].fillna('')

Output :

           contents              
categories    Bin 1   Bin 2 Bin 4
0                 A  Blanks   Buy
1                 B          Sell
2                 F              

Explanation :

Sorting based on None will give

           contents              
categories    Bin 1   Bin 2 Bin 4
0                 A  Blanks   Buy
1                 B    None  Sell
2                 F    None  None
3              None    None  None
4              None    None  None
5              None    None  None

Now select those rows where the all the values in a row is not null. So we can use ~pd.isnull(pm).all(1)(Here ~ is not operator which will covert false to true and vise versa). Which will give

0     True
1     True
2     True
3    False
4    False
5    False
dtype: bool 

Later boolen indexing to select the data i.e pm[~pd.isnull(pm).all(1)]

        contents              
categories    Bin 1   Bin 2 Bin 4
0                 A  Blanks   Buy
1                 B    None  Sell
2                 F    None  None

fillna('') will fill the none values with ''. Hope it helps.

Use:

#DataFrame from sample data
df_out = pd.DataFrame(df_out)

#filter columns names by list and test if NaN or None at least in one row
m = df_out[['aaa','bbb']].isna().any(axis=1)

#OR test both columns separately
m = df_out['aaa'].isna() | df_out['bbb'].isna()


#filter matched and not matched rows
df1 = df_out[m].reset_index(drop=True)
df2 = df_out[~m].reset_index(drop=True)
print (df1)
         name   aaa   bbb
0        Mick  None  None
1  Ivan-Peter     1  None

print (df2)
   name aaa bbb
0  Ivan   A   C
1  Juli   1   P

Another idea with DataFrame.dropna and filter indices not exist in df2:

df2 = df_out.dropna()
df1 = df_out.loc[df_out.index.difference(df2.index)].reset_index(drop=True)
df2 = df2.reset_index(drop=True)