Thanks to @cuomo860 who did a big update, Game Rule has been added which is set to on by default which means all executions are available, you can also disable it and then executions are set to be available with certain Character Traits, Executioner Court Position and other factors. Now everyone can use it the way they want.

All executions are now available for anyone no matter what your faith etc is.

Updated for 1.9 update thanks to @cuomo860