My guess is that it asks for the Opera user password, a kind of master-password, not your PC login info.

I have removed the specified website from the news-feed in the left-hand screen button, but it has absolutely no effect on the news I receive on the speed-dial page.
Also, I have different websites showing in the button news and the speed-dial news.

Maybe I have been ambiguous.
I am talking about the news page under the speed-dial.
You can't unsubscribe from a specific website, because you are not subscribed in the first place.
I just have a preference selected ("food", for example).

I would very much like to be able to blacklist websites from showing up in my News.
A specific website, "refinery29.com" shows up A LOT, with crap content, wrong labels (every single time).

Examples:
FOOD: Lady Gaga Dazzles With "Perfect Illusion," First New Single In Years
FOOD: Justin Bieber's L.A. House Is As Cool As You Imagined
FOOD: Here's What Happened When A Woman Emailed The Addresses In You've Got Mail
FOOD: You Need To See The All-Pug Version Of Stranger Things
FOOD: Kendall & Kylie Jenner Getting Stuck In An Elevator Is Why We Have Social Media
FOOD: Your Next Yoga Class Is A Flight Away
FOOD: Is This Fuller House's Newest Cast Member?
FOOD: Chipotle Will Test Delivery Drones At Virginia Tech
FOOD: Emily Blunt & John Krasinski Selling $3.5M Hollywood Hills Home

In all these examples (I have just checked for 2 min), only one is REMOTELY connected to food. REMOTELY!