I’m working on setting up a Google My Business profile for our Church and I’m wondering if it is possible.
Yes, it is possible. A Church and other Faith Centres can have a Google (My) Business Profile as you deal with “customers” and there is nothing in the guidelines against it.
Also, there are many Churches with verified Google My Business Profiles and Google made available several categories for Churches and other Faith Centres.

Top Tip: You can create a Gmail account for the church and apply for the profile. If you want to know how please check my guide: how to add a business to Google.
I hope this article helped you.
If you need further help, I am here for you. It does not matter if it’s your business or you are a professional that wants help with a client case: