Here is some interesting research from Nieman Lab - They asked a number of publishers about their experience with ad blocking on mobile and desktop, including two who are currently blocking content to people using ad blockers.
City AM, the UK free business newspaper, blocks content to anyone arriving on Firefox who uses an ad blocker. As you can see from the screengrab, they explain politely and clearly why they are doing it:
"In the first month or so since City A.M. began showing users the message, the percentage of readers using adblockers on Firefox has dropped by a third, Ashplant said. And about one-quarter of users who see the adblocking message actually turn it off or whitelist.
City A.M. also hasn’t seen a noticeable change in its bounce rate because of the new message, Ashplant said. He reads that to mean that people who decide not to turn off their adblockers likely wouldn’t have stayed on the site beyond reading that one article.
“It almost feels like the people who feel that it’s worth having that value exchange, and it’s worth turning the adblocker off — because they do want to see the content and they do perceive that City A.M. has got content that’s worth turning the adblocker off for — they’re inclined to spend longer on the site,” he explained. “It’s almost as if they’ve made a conscious decision that it’s worth doing it, and then they go on to explore the site and click on more than one page.”"
Be very clear about why you're doing it, and be polite, but firm.
I hear a lot about how people understand the value exchange in free content that is paid by ads (you look at the ads to get the free content), but in music for example there was a very long established and explicit value exchange (you pay money to buy a recording) that eroded very quickly.