For the "Browse by item" feature which allows users to search for unusuals by their cosmetic name and filter out any hats from unwanted classes (e.g. selecting scout to have scout only unusuals appear). The "Browse by effect" feature doesn't allow you to do this when you have selected an effect.
My suggestion is that once the user selects an effect they should be able to filter down what class they want that effect for resulting in all the unusuals with that effect for the specified class.
This implementation would allow users to easily find unusuals effects they want for their prefered class/multi class.