The first is to make sure you’re using the Following tab instead of For You. This tab is just tweets from the people you follow, so it doesn’t artificially favor Twitter Blue subscribers. You could also try blocking all retweets if you want to clean things up a little more.
If that’s not enough, you could try TweetDeck, the power user’s version of Twitter. This tool doesn’t have a For You page or any algorithmic sorting, meaning Twitter Blue users aren’t artificially boosted on it. TweetDeck is the one part of Twitter that’s completely untouched by the recent changes there, and I hope this doesn’t change. (So please, no one tell Elon Musk that TweetDeck still exists.)
Another cool extension, if you miss seeing legacy checkmarks, is Eight Dollars. Right now blue checkmarks only show up if someone is paying for Blue, meaning most people who had a checkmark prior to April 20, 2023 no longer have one. Eight Dollars can show you which users were verified before legacy verified checkmarks were removed, which is useful if you trusted the old system.
There’s a cat and mouse element to all of this, of course. Twitter’s current regime really, really wants to turn Blue checkmarks into sellable status symbols and any tool that diminishes the visibility of Blue subscribers cuts against that goal. They’re going to try to find a way to break this, and all similar, tools. For now, though, they work—use them while you can.