There is a drop argument in OneHotEncoder which you can pass a array to (one category to drop for each feature), can you use this for you use case? Adapting your snippet, something like this:

import numpy as np
import pandas as pd
from sklearn.preprocessing import OneHotEncoder

df = pd.DataFrame(['Male', 'Female', np.nan])
ohe = OneHotEncoder(drop=[np.nan])
ohe.fit_transform(df).toarray()

Output:

array([[0., 1.],
       [1., 0.],
       [0., 0.]])

I think the original request could be a convenience in some cases but it's a bit weird to have a drop strategy that depends on the lexicographical ordering of the categories.

For this particular case, I think @lesteve's solution is the right approach.

We could also offer to drop the "most_frequent" (and maybe also "least_frequent" although the latter is probably very unstable under CV/resampling) to drop a category based on its frequency in the training set.

Since the choice of the category to drop has an impact on the effect of regularization in a downstream linear model, dropping based on the frequency on the training set might be a good strategy to reduce collinearity for non-binary categorical variables in general.

Maybe @lorentzenchr has an opinion on this.

IIRC, R‘s formula drops the first level by default. That corresponds to our option "first". Having first, why not have an option "last". Edit: maybe not worth it.

More striking is the argument to have "most_frequent". This is a strategy that I‘ve seen in other GLM software. Model coefficients are then the effect relative to this most frequent level which seems the most natural choice (but is irrelevant for most other things).

We could also consider to support sample weights with "most_frequent", i.e. choose the level with highest sum of sample weights.

To the best of my knowledge, for linear models with penalties, one should never drop a level. For unpenalized linear models, the converse is true: always drop one level (otherwise one has perfect collinearity and solvers have a much harder job finding the unique minimum norm solution).

There is a (stalled) open PR for drop="most_frequent" here: #18679.

I agree it is not worth it to have a drop="last". The drop="most_frequent" feature is being tracked in #18553.