My read on the religion thing is that dominicans come in two classes:
religious evangelical type: women wear skirts,no sex, no disco, no drinking, etc... some dont even let the women shave their legs.
religious by lip service. may actually even attend church sometimes but dont really pay attention to it. Even those who havent been to church in 38 years claim to be catholic etc. You can sit outside a church and watch the "naughty" girls head in and then right out again to go play!
i haven't really met any who claim to be non-religious, non-christian, or agnostic. I think you would get a harsh reaction from most dominicans if you told them you were atheist. I am not saying they dont exist but everyone atleast pays lip service.
As far as dating goes, i doubt they would care too much what your beliefs are as long as you have some. If they were evangelical it would matter a lot, except you wont meet them unless you come down here on a mission or something.
We have jehova witness, mormen, 7th day adventist, pentacostal, open and closed brethern, and other evangelical groups active here. IF you actually belonged to one of those groups back home, you may find yourself welcome to visit them and you may find people to date there. You may be surprised at how much stricter they are here than in other places. You should expect to be accompanied buy an escort on your date etc......
I dont know of any buddist, muslim, or other religious groups active here. at least not way out where i live