Short answer to the "do I really need footwear in a public shower..." HECK YES! You cannot imagine what some people do in a shower...but you do NOT want to be walking in it...point made.
In 2014, I picked up a foot fungus at Orisson on my first night out. I failed to wear my shower shoes. Oh I had them with me, but removed them as I stepped into the shower...WRONG! Two weeks later, with feet that smelled like cheese and were very itchy, I finally asked a pharmacist and caused him to double over with laughter. He then promptly dispensed the apparently camino-standard foot ointment for "cheesy feet."
Everyone has their own thoughts on what is the best footwear to use for these showers. Some say to use something that, while waterproof, is also good to wear in the evenings or on off days when you are not wearing your hiking boots or shoes. Others, including me, bring a THIRD pair of footwear expressly for showers, and nothing else.
My now standard footwear to take on Camino no longer varies. I wear my Keen hiking boots, pack a pair of Ecco or Mephisto leather and nylon sports sandals, and just stick a cheap pair of flip-flops (zories, chacos, whatever) in my outer rucksack pockets. I buy the shower sandals in really bright colors at Oriental or China Bazaar shops for a couple of Euros. While stuck partially in the rucksack pocket they do double duty to alert oncoming drivers with a splash of neon color...
The truly neon colors ensure they do not get misplaced, are easily found, unlikely to be borrowed, and are inexpensive enough to be discarded or not lamented if they wear out or go missing. They also typically weigh very little.
I hope this helps.
