For the US, Giving is designed to track tax-deductible donations only. Any non-deductible transactions need to be processed in a different system and entered into your general ledger (Quickbooks, Peachtree, etc.) by another means.
For a payment to be tax-deductible, the person paying must receive no tangible benefit. Your organization may receive non-donation income from many different sources. For example:
The sale of baked goods at a fundraiser
A thrift store where all the proceeds go to a homeless shelter
Tickets to the youth summer camp
Reimbursement for the purchase of books by small group members
All of these types of transactions are instances where someone is receiving some physical goods or services, so they are not tax deductible.
For more on this topic, consult this IRS document: Tax Guide for Churches and Religious Organizations.
The way you process non-deductible donations is ultimately up to you, but we have a few suggestions:
If a donor wants to pay for a $100 Registrations event at your church and also make a $50 donation to the church, they will need to do this using two separate transactions--one sale and one donation. The donation portion can be processed and tracked in Giving.