You needn't be of strong faith to enjoy the peaceful atmosphere of Bishop Building. Inquire when the next service starts or when it's open for general viewing.
You're spoiled for sightseeing choice in Altstadtviertel. Bishop Building is a great place to kick off here, but there are plenty of other fine sights to discover. Linz Castle Museum, Lentos Art Museum and St. Martins Church are near the principal church and and will cap off your day nicely.