On the other hand a LLC does not provide anonymity like a trust can because it is filed with a state.

You can show yourself or if you want the anonymity of a real estate agent you can! 

In my experience most people don't get any anonymity for all kinds of reasons.

What are the best states to set up this entity with regards to taxes and anonymity?  

Finally, with the use of Trusts while establishing these structures you can add a level of anonymity by removing your name from public record.Actually operating an LLC does require some discipline, but it isn't rocket science.

(For some backstory, The Rainbow Bridge is the name of a famous (with pet owners) and incredibly powerful anonymously-written poem that brings great relief to bereaved pet owners.

Wy doesn't require the  secretary of state to be notified when the manager of an LLC changes  so you can utilize on nominee manager keeping your name off of any of the documents filed with the state for anonymity. 

And they largely rely on anonymity to protect you.

He even says its just anonymity 'hiding' that you own the LLC's. 

Hi Daniel,I’ve read if you’re interested in complete anonymity you can start by forming a holding LLC in Wyoming, New Mexico, Nevada or Delaware.