Yes, they give you shower shoes. No, everyone doesn't use them. Also, you are an active infection carrying individual coming into confined living quarters with upwards of 100 complete strangers from all walks of life. Athlete's foot is a fungus and is easily spread. Find the strongest over-the-counter remedy you can and use it religiously to kill that stuff.
You will be amazed or disgusted by the hygiene habits of your future shipmates.
I watched a guy wear his shower shoes to the shower, then leave them outside while he stepped in, barefoot, to the shower stall on ENTERPRISE back in 1995. Still makes my skin crawl.