This will be quite complicated because of the number of dropdowns you have but there is a pretty structured way to do the filtering. Assuming the column being used of the CrewNames list is called "CrewMember" and is a person type field.
In the items property of each of your dropdowns:
For the first dropdown:
Filter(
CrewNames,
IsBlank(Dropdown2) Or IsEmpty(Dropdown2) Or Not(CrewMember.DisplayName = Dropdown2.Selected.CrewMember.DisplayName),
IsBlank(Dropdown3) Or IsEmpty(Dropdown3) Or Not(CrewMember.DisplayName = Dropdown3.Selected.CrewMember.DisplayName),
IsBlank(Dropdown4) Or IsEmpty(Dropdown4) Or Not(CrewMember.DisplayName = Dropdown4.Selected.CrewMember.DisplayName),
IsBlank(Dropdown5) Or IsEmpty(Dropdown5) Or Not(CrewMember.DisplayName = Dropdown5.Selected.CrewMember.DisplayName),
IsBlank(Dropdown6) Or IsEmpty(Dropdown6) Or Not(CrewMember.DisplayName = Dropdown6.Selected.CrewMember.DisplayName),
...//And so on till you get all 12 of the others covered
Then for dropdown 2:
Filter(
CrewNames,
IsBlank(Dropdown1) Or IsEmpty(Dropdown1) Or Not(CrewMember.DisplayName = Dropdown1.Selected.CrewMember.DisplayName),
IsBlank(Dropdown3) Or IsEmpty(Dropdown3) Or Not(CrewMember.DisplayName = Dropdown3.Selected.CrewMember.DisplayName),
IsBlank(Dropdown4) Or IsEmpty(Dropdown4) Or Not(CrewMember.DisplayName = Dropdown4.Selected.CrewMember.DisplayName),
IsBlank(Dropdown5) Or IsEmpty(Dropdown5) Or Not(CrewMember.DisplayName = Dropdown5.Selected.CrewMember.DisplayName),
IsBlank(Dropdown6) Or IsEmpty(Dropdown6) Or Not(CrewMember.DisplayName = Dropdown6.Selected.CrewMember.DisplayName),
...//And so on till you get all 12 of the others covered
And so on for each dropdown box.
A couple of other notes. Doing it this way means that it won't matter the order in which users fill in the dropdowns, each time they open a dropdown, they will only see the crew that are left. Bonus tip- you can use the same filtering logic to use dropdowns as filters for galleries.