I just saw this picture get uploaded (https://e621.net/post/show/965827), and I have never really enjoyed this type of art style. I noticed the Japanese text and considered placing the japanese tag in my blacklist, but not all art with the tag japanese is in this particular art style.

How would I go about avoiding this art style in the future?

As a tip, you can enter post #965827 and it becomes a link (post #965827), allowing you to safely place a ) after it and not break it. It also helps people to click it regardless of which mode of the site they're on, as it runs /post/show/965827 instead of a full fledged url that will forcibly rewrite which version of the site they're on.

Well, one thing you can always do for any image is create a private set and then take the number from the end of that url and put set:xyz in your blacklist. This way you can add any individual images you don't like to the set (An option available during the post listings through the Mode dropdown menu!) and they'll be blacklisted.
Unfortunately, this requires you to manually add them to the set yourself, but unless it's the artist themselves you have a problem with, I don't think there's another option available.

Also consider blacklisting toony, maybe even big eyes. That one's severely undertagged, though.