When you protect the sheet, you are presented with a list of options that you would like to leave enabled. Among those is the list to enable AutoFilter, which will let you use the filter drop downs.
Unfortunately, Sort is a different matter. While it does appear as an option when you protect the sheet, it will only let you sort cells that are unprotected. As this is probably not the case for you, you may be stuck here.
Possible work around would be to create some short macros that do something like