Yes, on both the public and private (viewable on the portal) 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 is visible for filtering on this directory, while private means it will be hidden. The status selected for each item will be shown by a green unlocked icon (public) or red locked icon  (private) icon next to each value.

You can edit these values by clicking on the Paper and Pencil (Edit) icon next to the field. In the dialog box, you can change whether the category or committee is public or private by clicking on the Edit icon next to the name, then clicking on the Lock icon. Click on the Save icon to save the changes.

On the membership directory, the categories will automatically be included, but committees is an option that must be selected in the Directory Setup tab.

On the directory, the public values will display on the left side bar for filtering. Simply check the box next to the desired category or committee and the directory will update for members subscribed to that value.