Adam Danz had the right idea, but missed a few key things. The FilterIndex field should indeed have influenced the filter selection, but [presumably due to an internal Matlab bug] it does not get propagated to the internal com.mathworks.mwswing.MJFileChooserPerPlatform Java object. If you set this internal Java peer's FileFilterIndex field, the default filter is changed appropriately. Here's a complete working snippet:
First, set up the FileChooser object in memory (it will not be displayed):
filters = {'*.m'; '*.fig'; '*.doc'};
hFileChooser = matlab.ui.internal.dialog.FileOpenChooser('FileFilter',filters, 'Title','Select your file:');
All of the input parameters to FileOpenChooser are optional - they just need to come in P-V (propertyName,value) pairs. The available parameters are Title, InitialPathName, InitialFileName, FileFilter, UseNativeDialog, MultiSelection (there are also a few other undocumented fields but they are not relevant here).
Next, access the FileOpenChooser's underlying Java peer object using the undocumented Peer property and set its FileFilterIndex field:
hWarn = warning('off','MATLAB:structOnObject');
jFileChooser = struct(hFileChooser).Peer.java;
warning(hWarn);
jFileChooser.setFileFilterIndex(1); % this sets the 2nd index (='*.fig')
Note that Java indexing starts at 0, so index #1 means the 2nd filter (*.fig in this example).
Now display the modal dialog, wait for the user's selection and get the results:
hFileChooser.show();
selectedFileName = hFileChooser.FileName; % 'abc.fig' for example
selectedPathName = hFileChooser.PathName; % 'C:\path\to\file' for example
selectedFilterIdx = hFileChooser.FilterIndex; % the eventual filter index used by the user (first=1)
selectionState = hFileChooser.State; % -1=initial; 0=dismissed without selection; 1=file was selected
delete(hFileChooser); % clean-up memory
