Upvote/downvote toggle
One thing I noticed is that you're passing this.handleUpvoteClicked.bind(this) as a prop to your FlatButton components. The problem is that the call to Function.prototype.bind creates a new function instance for both click handlers every time your Post renders, meaning your FlatButton components see a different value (function reference) being passed in as a prop, and they'll also re-render. Probably not a big deal for your simple setup, but it's something to keep in mind for later, because it can drastically affect performance for bigger apps.

The solution is to bind your methods in the constructor. That way .bind(this) is only called once during construction (good because that method is a little slow), and your components will see a consistent function reference being passed in as a prop and will know they don't have to re-render.

I also tweaked your conditionals inside the click handlers a bit, so that they only run if the button isn't disabled.

Here's what I came up with:



import React, { Component } from 'react';
import { Card, CardText, CardHeader } from 'material-ui/Card';
import FlatButton from 'material-ui/FlatButton';

class Post extends Component {

  constructor(props) {
    super(props);

    this.state = {
      disabledUpvote: false,
      disabledDownvote: false
    }

    this.handleUpvoteClicked = this.handleUpvoteClicked.bind(this);
    this.handleDownvoteClicked = this.handleDownvoteClicked.bind(this);
  }

  handleUpvoteClicked() {
    if (!this.state.disabledUpvote) {
      this.setState({
        disabledUpvote: true,
        disabledDownvote: false
      });
    }
  }
  
  handleDownvoteClicked() {
    if (!this.state.disabledDownvote) {
      this.setState({
        disabledUpvote: false,
        disabledDownvote: true
      });
    }
  }

  render() {
    const { content, createdAt, votes } = this.props.post;

    return (
      &lt;div className="post-container"&gt;
        &lt;Card&gt;
          &lt;CardText&gt;
            &lt;p className="timestamp"&gt;
              {moment(createdAt).fromNow()}
            &lt;/p&gt;
            {content}
            &lt;div style={{ textAlign: "right" }}&gt;
              &lt;FlatButton 
                label="Upvote" 
                primary={true} 
                disabled={this.state.disabledUpvote}
                onClick={this.handleUpvoteClicked} /&gt;
              &lt;FlatButton 
                label="Downvote" 
                secondary={true}
                disabled={this.state.disabledDownvote}
                onClick={this.handleDownvoteClicked} /&gt;
            &lt;/div&gt;
          &lt;/CardText&gt;
        &lt;/Card&gt;
      &lt;/div&gt;
    );
  }
}

export default Post;