First idea is convert columns to datetimes, get difference and convert timedeltas to days by Series.dt.days:
df['Diff_in_Days'] = (pd.to_datetime(df['End_Date'], format='%Y%m%d')
                        .sub(pd.to_datetime(df['Start_Date'], format='%Y%m%d'))
                        .dt.days)
print (df)
   Start_Date  End_Date  Diff_in_Days
0    20201101  20201130            29
1    20201201  20201231            30
2    20210101  20210131            30
3    20210201  20210228            27
4    20210301  20210331            30
Another solution better if processing datetimes later is reassign back columns and use solution above:
df['Start_Date'] = pd.to_datetime(df['Start_Date'], format='%Y%m%d')
df['End_Date'] = pd.to_datetime(df['End_Date'], format='%Y%m%d')
df['Diff_in_Days'] = df['End_Date'].sub(df['Start_Date']).dt.days
print (df)
  Start_Date   End_Date  Diff_in_Days
0 2020-11-01 2020-11-30            29
1 2020-12-01 2020-12-31            30
2 2021-01-01 2021-01-31            30
3 2021-02-01 2021-02-28            27
4 2021-03-01 2021-03-31            30