Why is Adobe Premiere not letting me apply a filter to this sound clip?
Check to see if the filter is restricted to specific audio file / stream / track types. 

For instance, I believe you’ll get the same issue if you tried to drop filters that apply only to Stereo Tracks to a Mono File Track, such as Swap Channels, Fill Left, Fill Right, etc. Because its impossible to swap left and right channels when youre on a mono track. 

You dont specify what filter, but thats my guess. 

Same goes with Video Filters... there are some filters you cant drop onto video tracks with Alpha, or vice versa.