There is no way to stop this, and it's maddening, but the saving grace is that, at least in many cases, you can just dismiss these.
John_C21 is correct that with the ubiquity of adblockers websites are now including code that detects that you're using them and gives you nags like the one you've shown because, essentially, they rely on ad revenue to provide content and you're blocking it.
What makes me crazy is that web advertising is just so much more intrusive than print advertising on the whole and always has been. If what were being presented were similar to the print ads that you see in a newspaper or magazine I could just ignore them the same way I do in print media. But most ads online blink, scroll, flash, play music, have video, or similar and they are just infinitely more annoying and draw attention from actual content. You'd think that the powers that be would have figured out by now that this is the primary reason that adblockers have come in to extremely widespread use, but they haven't.
For websites that won't allow me to continue with an adblocker on I keep MS-Edge on my machine without an adblocker so that if there's something I really think I need or want to see in a given situation I can. Otherwise I just write off that website as one I will not visit again, even if I've been using it for years. While I understand the concept of web advertising it should be like other advertising in print media and where advertisers know that what they're paying for is placement. There are lots of times where that placement will not result in "eyes on" attention and, to me, adblockers are the same as me not granting my "eyes on" attention.
I'll probably end up an old man who can only view two websites on the worldwide web if this trend continues, but if so, so be it. I'm not about to deal with the kind of visual and auditory distractions that are served up as web advertisements.
Brian AKA Bri the Tech Guy (website in my user profile) - Windows 10 Home, 64-Bit, Version 1803, Build 17134
In a modern society where everyone thinks their opinion deserves to be heard nothing annoys me more than individuals who mistake their personal preferences for fact.
~ Commenter TheCruyffGurn on the The Guardian website, 8/13/2014