Does it make sense to apply recursive feature elimination on one-hot encoded features?

Does it make sense to apply recursive feature elimination on a feature set pre-processed with One-Hot Encoding?

This is my code for feature selection:

xgb = XGBClassifier(n_estimators=100,
objective='multi:softprob',
num_class=4,
random_state=42)
rfecv = feature_selection.RFECV(estimator=xgb,
step=10,
cv=model_selection.StratifiedKFold(2),
scoring='f1_weighted',
n_jobs = -1,
verbose = 2)
rfecv.fit(X_train, y_train)


DataFrame X_train contains both continuous and categorical features. Categorical features are one-hot encoded, while continuous features are passed through MinMaxScaler.

I am not sure if it makes sense to eliminate one-hot encoded columns using RFECV. Maybe I should run RFECV on continuos features only? Or I should apply one-hot encoding somehow at each iteration of RFECV?

No, it does not make sense. If you have a categorical variable Cat with 10 levels A, B, C,..., J that you one-hot encode, then the variable is Cat, and if you want feature selection, you should choose Cat or omit Cat, with all or none of its one-hot-encoded columns. Omitting just some of the columns will change the meaning of the model/variable.
More concretely, if you as usual drop one of the columns as a reference level, say A, and then later your feature extraction is dropping C, that makes the model assuming that levels A, C acts identically, and that might be wrong. Also, if you at the outset choose some other reference level, that might lead to very different results.