Datetime accessor fails on cftime arrays with missing values

What happened:
I have a computation that output dates but that sometimes also outputs missing data. (It computes the start date of a run in a timeseries, if there is no run, it outputs NaN). Afterwards, I'd like to convert those dates to dayofyear, thus I call out.dt.dayofyear. In a case where the first value of out is missing, it fails.

What you expected to happen:
I expected out.dt.dayofyear to return an array where the first value would be NaN.

Minimal Complete Verifiable Example:

import xarray as xr
import numpy as np

da = xr.DataArray(
    [[np.nan, np.nan], [1, 2]],
    dims=('x', 'time'),
    coords={'x': [1, 2], 'time': xr.cftime_range('2000-01-01', periods=2)},
)
# out is a "object" array, where the first element is NaN
out = da.idxmin('time')

out.dt.dayofyear
# Expected : [nan, 1.]

Got:

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-56-06aa9bdfd6b8> in <module>
----> 1 da.idxmin('time').dt.dayofyear

~/.conda/envs/xclim-dev/lib/python3.8/site-packages/xarray/core/utils.py in __get__(self, obj, cls)
    917             return self._accessor
    918 
--> 919         return self._accessor(obj)
    920 
    921 

~/.conda/envs/xclim-dev/lib/python3.8/site-packages/xarray/core/accessor_dt.py in __new__(cls, obj)
    514         # do all the validation here.
    515         if not _contains_datetime_like_objects(obj):
--> 516             raise TypeError(
    517                 "'.dt' accessor only available for "
    518                 "DataArray with datetime64 timedelta64 dtype or "

TypeError: '.dt' accessor only available for DataArray with datetime64 timedelta64 dtype or for arrays containing cftime datetime objects.

Anything else we need to know?:
This also triggers computation when da is lazy. A lazy .dt accessor would be useful.

The laziness of it aside, would it be meaningful to change:
https://github.com/pydata/xarray/blob/d4b7a608bab0e7c140937b0b59ca45115d205145/xarray/core/common.py#L1822
to cycle on the array while np.isnan(sample) ?

Environment:

The failure is raised while validating the .dt accessor in xarray/core/accessor_dt.py, with the referenced array check in xarray/core/common.py. Reproduce the supplied cftime example, then make the accessor handle a leading missing value without losing cftime detection; verify that the result is [nan, 1.] and consider the noted lazy-array behavior.