I strongly believe that you can embed the culture of the people in the organisation you serve within your service design work. As I'm working a lot with a church these days, I try to use spirituality and faith when facilitating workshops for that organisation. Here are a few things I've used in the past:
Dot voting with spirituality: give everyone three personal dots to vote, and let people know they can draw one or multiple circles when they feel there is something spiritually inspired. Once the vote is finished, if there are "circles of spirituality," people share why they have put the circle with the rest of the group.
Pray or meditate before key activities: before ideation or decision moments, prayer or meditation can help inspire people.
Use spiritual music: use music that comes from that spiritual practice as background music when people work in silence.