Should the type of Boolean categorical features be numerical or categorical after encoding?
In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively. Generally, gender can not  be considered  - true or false . Classification is based on sex - Male or female  . Categories differ and can be assigned particular  numerical values (dummy variable) 1, 2 or 2, 3 etc. Binary variable is different. If you want to find correlation  between  the scores obtained by Male students and female students,  you will have to have matched pairs. Categories measure the levels for grouping. Binary classification can be undertaken for a dependent  variable in regression analysis or point biserial correlation. The standard softwares for statistical analysis do not invoke 0,1 as variable. The probability based solutions may use this classification for grouping.