I see you asked this awhile ago, but hope a reply is still helpful.
I gave birth to my dd there Dec '06, and it was a wonderful experience! They were absolutely fine with us declining all newborn shots/procedures you mentioned. She was born in the water, and the midwife actually caught her (the doc was holding the flashlight as the lights were dim--so yeah, the doc was ok with being hands-off).
I can't give you much info on laboring there, since I was complete on arrival! We live 1 1/2 hours away, and I travelled there for prenatals and classes. It wasn't much of a hardship, since we live in a tiny town, and I used the opportunity of being in the "big city" to do my Christmas shopping. Labor in the car wasn't a big deal. I just told myself I would NOT go too fast and have the baby on the way. And I didn't. I hit transition as we entered the parking lot.
I felt like getting out of the tub to deliver the placenta, so they helped me move to the bed. And waited until I was ready to push to deliver it. We then waited for the cord to stop pulsing to cut it. Oh, and they did not suction baby after delivery--they feel babies are pretty good at clearing their own gunk, and only interfere if it seems baby needs the help. She was placed immediately on my chest and towels put over us to keep her warm.
I had a tear along my old episiotomy scars, which they were going to leave alone, but I had some extra bleeding, so they wanted to stitch that and see where we were after that. They have all the meds available for pp bleeding that are available in the hospital if that is a concern.
For me, they didn't work, and I kept bleeding, so we made the decision to transport to the hospital. The doctor met us there, I was admitted as her patient, with ob consult. The baby was never admitted and never left our sight. I had retained fragments that had to be cleaned out with a manual d&c. So nothing the center could have done differently to prevent.
I would recommend their services to anyone, even if you have a bit of a drive to get there. And will definitely go back (if they don't risk me out--and the mw there said they would likely take me again) if we are blessed again.
They definitely trust birth, and trust a mom to know what her body and baby needs during birth. They are there to support you and offer suggestions, or get out of your way and let you do your thing.
And the feeling when you walk in the door is just serenity and peace.
A really nice place to bring a new life into the world.