According to [1] first, you must become a member by invitation, and you need "undoubted Catholic morality and practice" and to show "merit over the years with regard to the Order of Malta, its institutions and its humanitarian works"
They only issue passports to people in charge of specific projects. Of about 13k members there are about 500 passports, almost entirely held by their diplomats or their governance members.
Also, they’re still an order of catholic knights :)
