What to use for NaN Pandas when comparing with dates?

Question

I have a pandas Series of NaN's and dates

eg.

# In the codebase this is being generated and used elsewhere, so changing the format would be a pain
x = pd.Series([
   np.nan, 
   np.nan, 
   pd.to_datetime('2020-01-01').date(),
   np.nan,
   pd.to_datetime('2020-02-01').date()
])

The questions is whether the most recent date (if there is one) is greater than '2021-06-01'

I can't do

x.max() > pd.to_datetime('2021-06-01')

because x.max() returns TypeError: '>=' not supported between instances of 'float' and 'datetime.date'

This is because pandas does not want to compare the float np.nan to a date.

However, if I do x.fillna(pd.NaT).max() it is still unhappy and throws warnings that np.NaT should not be compared to dates.

What is the appropriate way to do this in Pandas.