I did laundry at YC a couple of weeks ago, in the first-floor laundry room near room 1067 (the laundry room in the man building -- not the laundry facilities in the separate building by the quiet pool). They did have a vending machine which contained both regular and allergy-sensitive detergents, just as shown in the photo here:
https://www.resortsgal.com/resorts/laundry-disneys-yacht-club/.
However, if sensitivities are an issue for you -- as they are for a couple of my family members -- you might want to consider packing your own fragrance-free detergent sheets, which is what I did, just to ensure I'd have them even if the vending machine didn't, or in case it was out of order. I just slipped them into a quart-sized Ziploc baggie with a couple of dryer sheets from home and the fabric laundry sack left over from my college days, and voila! -- I had a complete "laundry kit" that was practically flat and took up no space at all in my luggage. (We travel carryon-only, so suitcase space is always at a premium.)
The detergent sheets I used were Vacplus brand, purchased from
Amazon, but there are several brands on Amazon (and probably in your local store) that offer fragrance-free detergent sheets that are well-rated.