Since version 3.0.2, it is now possible to enable remote libraries for Advanced Custom Fields (ACF) front-end forms. To do so use this filter like this for example:

function enable_remote_libraries() {
	return current_user_can('upload_files');
add_filter('acf_form_enable_remote_libraries', 'enable_remote_libraries');

Note that since ACF only shows the media library to users that have the upload_files capabilties, it is only possible to enable the remote libraries for these users as well.