Apple Wallet without Apple Pay?

Add and manage passes in Wallet on iPhone - Apple Support, please note that passes cannot be directly added within wallet, except for QR code enabled passes. For everything else, its done either through the associated app, an email, airdrop or a link in a website.

To add something like a membership to Wallet, you don’t tap the + icon in Wallet. You should be able to hit back or cancel to I presume a mostly white screen that just says “Wallet” at the top. To add a membership pass to Wallet see the following:

On iPhone or iPod touch

• Use Wallet-enabled apps (Scroll down in Wallet, tap Edit Passes, and tap Find Apps for Wallet).*
• Scan a barcode or QR code (Scroll down in Wallet, tap Edit Passes, tap Scan Code, and scan with your iPhone camera).*
• If you pay with Apple Pay at a supported merchant and you get a notification, tap the Wallet notification.
• Use Mail or Messages.
• Go through a web browser.
• Share through AirDrop.
• Use your Mac.
• Create an iTunes Pass.
• For student ID cards, use your school's student account management app.

If you don't see the option to add a card, ticket, or other pass to Wallet, contact the merchant to make sure that they support passes in Wallet.