How difficult is it to be an anonymous site owner?

I would like to create a website with a very radical political message. It won't be unethical (encouraging violence, etc.), but I feel that the items I plan to list will definitely make me more enemies.

How difficult would it be to protect my identity from anyone finding out who I am? I know that domains always have the option of $10/year to privatize your registration information, but is there any other protection that I should think about?

You need to take some time to determine and then explain how anonymous you intend to be. Just hiding your name, for example. Whois protection is not going to do that. This will help some, but it may take more.

Resume
Minimizing attack vectors by not registering a domain, not registering a hosting service, not using a credit card associated with your name, not disclosing your IP address and email address, not using Google Analytics and not discussing your new project will reduce the chance of revealing your identity.

How can your identity be discovered?
To understand how to set up a website anonymously, you must first assess that your identity can be obtained through:

A WHOIS record for any domains that you register.
Your IP address (sent in the header of the emails that you send and find in the server logs).
Accounts of your service providers (i.e. hosting, domain registrar, Internet Service Provider).
Your email address.
Your credit card details or other payment method.
Information about your Google Analytics account (if you are tracking more than one site).
How can you eliminate most of these things?
The easiest and best way to eliminate many of these things used to identify you is:

Don't register a domain or pay for hosting at all.

Instead, sign up for a free blogging platform such as Tumblr or WordPress.com which provides you with a subdomain when registering (i.e. yoursite.theirbrand.com ). Many bloggers and human rights activists choose this option because the main thing they have to worry about is protecting their email and IP address.

You can protect your IP address to a certain extent by using a VPN, such as HideMyAss, when connected to the Internet or using the Tor network. You must enable a VPN or Tor connection before registering for any services and while using them.

A search for an "anonymous email address" will provide you with an address that you can use to register anonymously with the services.

Keep in mind that some free blog providers remove blogs that may seem offensive. Read their terms and conditions before registering and create backups of your content if it is important to you.

If you feel the need to register a domain and buy hosting
If for any reason you need to register a domain and buy hosting, consider the following ways to protect your information:

Register the domain using an anonymous registration service (not like domain privacy) as indicated in this question.

Use anonymous hosting, which allows you to register under a pseudonym and without specifying an email address, for example Anonymous Speech.

Consider using hosting and registration services that support prepayment methods that do not link your identity to the payment method (for example, cash). As always, be careful when sending cash by mail.

Consider registering a domain in a country outside your country's jurisdiction and hosting your site somewhere else. This does not prevent requests for information from being sent to hosting providers, but it can add an additional barrier.

Each of these items alone will not protect your identity from someone who decided to discover it, but together they will make it difficult to figure out who you are.

Be careful when using Google Analytics and other third-party services
If you use Google Analytics - even on a host platform like tumblr - you should know that it is possible to perform a "reverse Google Analytics ID scan" by putting your site's URL into services like eWhois and Statsie to find out which other websites you are tracking with the same account a Google Analytics account. This can potentially expose you if you don't protect your identity on other sites that you use.

For this reason, avoid using Google Analytics or any third-party services that may be used to identify you. A blog using the main theme, without add-ons, widgets, or additional third-party scripts that require registration elsewhere.

Choose a unique nickname
If you are going to blog under a pseudonym, make sure that you have never used that pseudonym for anything else. The aliases that you used on forums many years ago ('runningWithScissors') tend to appear in search results.

Don't chat offline
Also, try not to tell anyone what you're doing. There's no point in taking steps to disguise your identity online if you're willing to give it away offline for free.