Two array_agg at once
That should be simple with array_agg and additional FILTER clauses:

SELECT 
    posts.id, posts.content, users.name as author
    array_agg(likes.user_id) FILTER (WHERE likes.is_liked) as likes,
    array_agg(likes.user_id) FILTER (WHERE likes.is_disliked) as dislikes
FROM posts
   INNER JOIN users ON posts.user_id = users.id
   INNER JOIN likes ON likes.post_id = posts.id
GROUP BY posts.id, posts.content, users.name;