It would be easy to think that “pull out all the stops” entered into the English language by way of sports, given how often that phrase is used by sports announcers (and the fact that there’s even a “shortstop” position in baseball). The phrase, however, entered English by way of music—specifically through terminology used by organists.
An organ stop is a component of a pipe organ that regulates the flow of air to the pipes. There are multiple stops and skilled organists will adjust the stops to help create that multiple-instruments-playing effect that organs are known for. To “pull out all the stops” is to adjust the stops for every rank of pipes in the organ and would indicate that the organist is playing a complicated and crowd pleasing piece that requires the entire range of pipes available to them. The phrase jumped to general usage where it now means to use every available means to achieve your goal (just as the organist uses every available pipe to play the piece).
Image courtesy of the United States Naval Academy.