Some freeze proof hose bibbs have a "loose fitting" spacer piece inside the tube, in order to keep the sealing washer centered on the seat when it closes.
You can see on this arrowhead replacement stem, it's a square shaped metal piece right next to the washer (on the right side of the picture.) In my experience, this metal spacer "squeaks" when turning on and off the hose bibb, and make some odd "fluttering" noises when water is flowing, from the metal spacer inside scraping & vibrating inside the metal tube.
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I don't know if your hose bibb has a loose fitting metal spacer inside it as well, but if so that might be the source of the squeaks.
I happened across this picture, which looks like it's got a rubber spacer (maybe also a backflow preventer...) which would surely be more quiet than the metal spacer.
PS - I have the arrowhead hose bibb with the square shaped metal spacer and although a bit noisy, it does work very well. (It has a really strong water flow.) Hope this info helps.