I have a data set with different feature types (numerical and categorical). I applied one-hot-encoding to the categorical features and then used ANOVA to find most relevant features. 6 of 66 features in total produce a result that almost as good as when using all feature. These 6 contain 3 numeric and 3 (binary features - which are result of one-hot-encoding). The results are good and I showed which feature are most relevant but the question is whether it was okay to apply ANOVA to these binary features?
There is nothing specifically about one-hot encoding that makes ANOVA inappropriate.
Most software (certainly R and SAS) does some version of coding of categorical variables for you. With R and SAS (and maybe others) you can choose among various parameterizations for categorical variables (effect coding, dummy coding, Helmert contrasts etc.)