It's a rule at Disneyland too, but they are more lax about it there. They will allow bottle feeding if no other nursing moms need the chair you are using. If they are busy and you are the only mom not nursing and one comes in, you have to give up the rocker and move. I did a combo of breast and bottle feeding. I would nurse first and then take the bottle out of the cooler bag and give my son the bottle next. Luckily he didn't mind cold bottles!
I actually think it's a fair rule. You can feed a bottle anywhere at WDW. Nursing moms deserve some privacy if they wish. Of course everyone would like to relax, but those centers are not meant to cater to every single parent with a baby at the parks.
Actually, as being 'baby care centers' I would think they ARE meant to cater to every single parent with a baby in the parks. I think it is horrible that a bottle feeding parent would be turned away. My goodness, what next - only cloth diapering parents allowed to use the changing tables there??
If I still had a bottle feeding baby - you could count me among those calling LOTS of managers/supervisors to complain about this one. Bottle feeding parents already get a lot of flack - this is just one more slap in the face.