I notice that if I open a new private Opera browser window and then navigate to ebay.com, after an initial "dangerous" icon appears in the address bar, the secure connection icon appears and I am able to sign in to eBay without further issues.
Returning to the regular (non-private) Opera browser window, I am now able to sign in without getting a warning.
Previously I erased my eBay cookies in Opera and restarted the browser, though I am not sure if those two things were related to being able to sign in later -- but they might be worth a try if you are still experiencing an issue.
