The days of pulling out your wallet and tediously typing in credit card numbers are long gone. Google will happily save your card details to make it easier to splurge on internet shopping, and of course, to pay for Google services. Chrome is getting deeper payment integrations, which are now separate from Chrome Sync.
Previously, you could only access saved card information in the browser if Chrome sync was turned on. Now, you just have to be logged in with a Google account to get payment auto-fill. As Google points out, signing into a Google website will sign you into Chrome so you can access your saved cards. However, that doesn't enable Chrome sync.
You can still add payment methods to Chrome and keep the data local without enabling sync. In either case, you'll just have to verify CVC numbers to use your saved cards. If you prefer to disable Chrome sign-ins altogether, that's available under Settings > Advanced > Allow Chrome sign-in.