If you only want volunteers to see the schedule for their own ministries in the app, you can do so by making all of the ministries in MSP private.
1. Navigate to the Ministries tab in MSP
2. Select a ministry, and then click "Edit Ministry..."
3. Mark "Keep assignments in this ministry private" and click OK
4. Repeat for every ministry
Once you do this, when volunteers click on the Full Schedule tab and select "All Volunteers", they will only see those scheduled in the ministries to which they belong.