Yes, on both the Public and Private versions of the Membership Directory a person can filter for Members based on which Categories or Committees those Members are subscribe too. The filtering options will always be available however you do have control over which Categories or Committee values are visible for filtering. When editing the Category or Committee values within any Constituent's record you will be able to set a Public or Private status for each value. Public means it can be filtered for on this Directory, while Private means it will be hidden. The status selected for each item will be shown by a Green unlocked (Public) or Red locked (Private) Lock icon next to each value.
Then on the Membership Directory these Public Category and Committee values will display on the left side bar for filtering. Simply check the box next to the desired Category or Committee and the Directory grid will update for Members subscribed to that value.