Filter out Early Access games from Steam store
Solution 1:
With the new released update, you can actually hide Early Access Games from the carousel and the "Recently Updated Box" as well as the "New Games on Steam" Box.
Just click the little customize box and you can choose what to see there. In the carousel, this box only appears once you mouse over it.
Solution 2:
Steam hides early access games from the "new releases" section of the store and provides a dedicated Early Access page to find new early access games. However, there isn't a general feature available in either the Steam client or the store website that allows you to completely remove early access games from the store.
Solution 3:
This is now something you can disable by clicking your username -> Preferences -> Uncheck "Show Early Access titles"