Hi there,
the sort filter is also using the search-item class on its sort by select elements. Which is the class that GP uses for its Navigation Search.
Its not currently possible for us to filter our Javascript to change the search-item class to something else. So you would need to disable the navigation search. You could always hook in a different search widget into the nav.
The plugin developer should also note that the search-item class is used with the core WordPress search forms. Which means it may conflict with over types of search plugins. It might be something the plugin developer should change to make it specific to their needs.