Hmm. Possibly a little off the topic ...
I compose for 1x1 with all my cameras quite often, but I never set a camera to 1:1 framing. I can figure the crop in my imagination and set Lightroom to automatically crop all the images once I import them ... that way I have more data and can tweak the crop a little side to side if needed.
I have no idea what the Fuji does when you set the cropping. With most cameras, it sets the dimensions in the raw data file and adjusts the LCD/EVF view.
Once upon a time with 35mm SLR cameras, I bought a spare focusing screen and used silver tape to block off the portion of the frame to give me a square crop ... ;-)