How to render random objects from an array in React?

I went ahead and created a working example for you

import React from 'react';
import { Link } from 'react-router';

function shuffleArray(array) {
  let i = array.length - 1;
  for (; i > 0; i--) {
    const j = Math.floor(Math.random() * (i + 1));
    const temp = array[i];
    array[i] = array[j];
    array[j] = temp;
  }
  return array;
}

class RecommendedPosts extends React.Component {
  render() {
    const shuffledPosts = shuffleArray(this.props.posts);
    return (
      <ul>
        {shuffledPosts.map((post) => {
          return (
            <li key={post.id}>
              <p>{post.title}</p>
              <p>{post.text}</p>
              <p>{post.category}</p>
              <Link to={`/blog/post-1/:${post.id}`}>Weiter lesen</Link>
            </li>
          );
        })}
      </ul>
    );
  }
}
RecommendedPosts.propTypes = {
  posts: React.PropTypes.array,
};
export default RecommendedPosts;

Bonus tip - since you're not using state or lifecycle, you can create a much simpler functional component as such:

import React from 'react';
import { Link } from 'react-router';

function shuffleArray(array) {
  let i = array.length - 1;
  for (; i > 0; i--) {
    const j = Math.floor(Math.random() * (i + 1));
    const temp = array[i];
    array[i] = array[j];
    array[j] = temp;
  }
  return array;
}

function RecommendedPosts({ posts }) {
  const shuffledPosts = shuffleArray(posts);
  return (
    <ul>
      {shuffledPosts.map((post) => {
        return (
          <li key={post.id}>
            <p>{post.title}</p>
            <p>{post.text}</p>
            <p>{post.category}</p>
            <Link to={`/blog/post-1/:${post.id}`}>Weiter lesen</Link>
          </li>
        );
      })}
    </ul>
  );
}
RecommendedPosts.propTypes = {
  posts: React.PropTypes.array,
};
export default RecommendedPosts;

In your Recommended post first shuffle the posts and store it in state and then render

import React from 'react';
import { Link } from 'react-router';

class RecommendedPosts extends React.Component {

constructor() {
super(props);
this.state = {
posts: this.shuffle(this.props.posts)
}
}

shuffle(posts){
 ///shuffle using some algo
return posts
}

render() {
return (
  <ul>
    {this.state.posts.map((post, idx) => {
      return (
        <li key={idx}>
          <p>{post.title}</p>
          <p>{post.text}</p>
          <p>{post.category}</p>
          <Link to={`/blog/post-1/:${post.id}`}>Weiter lesen</Link>
        </li>
      );
    })}
  </ul>
);
}
}
RecommendedPosts.propTypes = {
posts: React.PropTypes.array,
};
export default RecommendedPosts;