Before you Tweet, you’ll be able to choose who can reply with three options: everyone (standard Twitter, and the default setting), only people you follow, or only people you mention. Tweets with the latter two settings will be labeled and the reply icon will be grayed out so that it’s clear for people if they can’t reply. People who can’t reply will still be able to view, Retweet, Retweet with Comment, and like these Tweets.
Predictably, a bunch of tweets immediately rolled out daring folks to reply (with a greyed out reply button making it impossible), or taunting them about their inability to reply. Some came from Twitter itself. Some folks found the bits funny, others not so much.
Nonetheless, good to know the thinking behind all this. This is a limited rollout, so only some people have the ability to limit their replies.