Yeah - they need to change her! For that time period, if it were me, and I use cloth diapers and cloth wipes most of the time, I would do the following:
1) Treat them like a daycare for this purpose because they are going to get the same training/info your local daycares will get. Many church nurseries, if not all, follow the same guidelines as far as changing diapers, trash disposal, snack time, cleaning, etc as the daycares do. I know my small church, back in the 90's, went through major changes so it could follow state standards. The RDA has a tip sheet for helping you use cloth diapers in a daycare.
2) Try to educate them. Explain that a cloth diaper does not wick away the urine like a disposable does and that your child needs to be checked/changed more often. A newborn - every hour regardless of the type of diaper. Tell them how long she usually stays dry every other morning of the week if it is not 3 hours ;)
3) If the above does not work, see if they are open to a disposable insert inside a cloth cover (which would be so silly if they would take that over an AIO) because that could save you some money.
4) Buy disposables.
Our daughter will start the nursery for the first time on Sunday. We've kept her with us until now so I am about to be in this boat. I go to a huge church yet very few cloth diaper, and I may be the only one that does 100%. I am sure it will be interesting since she poops during that time every day!