For centuries, until the Renaissance, pretty much all art was commissioned by religious authorities. Churches, temples, mosques, paid artists and musicians and poets to celebrate and illustrate their particular faith. Now things have pretty much reversed, and most art is produced outside of the religious context.
Yet a healthy percentage of contemporary American poetry is based on spiritual feelings, if not overly religious ones. However, the market devoted specifically to publishing spiritual poetry is minuscule. It's much more common to see poems with spiritual undertones in academic and independent literary journals than the few journals that are focused on spiritual art.
Because I'm interested in writing and reading spiritually-based poetry, I've looked into the few litmags that focus on this subject matter. While I don't think a literary magazine should restrict itself in terms of subject matter, I think these few (and any others you can suggest) have come into being because this subject matter has been often excluded from the generality of literary publishing. Here are a few magazines that focus on contemporary spiritual poetry:
And for online anthologies of spiritual poetry from all ages:
Undoubtedly, there are more that I don't know about. Suggestions are welcome! Maybe I'll start a page on my website if I get enough listings. But hopefully the mainstream literary journals will increasingly include overtly spiritual poetry. It does seem to be tending in that direction.