Do you need to know music theory in order to fully appreciate Free Jazz? What is it that makes free jazz harder to understand than, say Bebop?
Some genres and styles (not exclusive to jazz) are based on very well stablished and known patterns and dynamics: specific cadences, progressions, scales, rhythms, instruments, etc.
Free jazz is a very loose concept that tries to label improvised performances that try to cut away those common conventions. As you walk into the realm of the uncommon, things start to sound strange.
Do you need to know music theory in order to fully appreciate Free Jazz?
It depends on what you mean by "fully appreciate". If you want to analyze a performance and study what is happening, why, and how, then music theory will be helpful. But if you want to just listen and enjoy, then music theory is unimportant.
I've played free jazz tracks to friends with zero music theory knowledge, and some of them have loved it to the point of starting a free jazz music collection. Other friends, including people that make a living out of music, have given me the "what is going on, I don't want to listen to this" look.
What is it that makes free jazz harder to understand than, say Bebop?
Many genres and styles are based on patterns that are familiar to the listeners. Bebop in particular has a bit blues, swing, gospel, ragtime, and theory that can be tracked all the way to the common practice period (baroque, classical, and romantic).
Free jazz tends to say goodbye to many of those patterns, so you can find it harder to understand. The idea is to free yourself from those conventions (both as a musician and listener), and explore what is beyond those limits.
It can get chaotic (not necessarily), as musicians can all be playing different harmony, rhythm, and perhaps no other framework than "no framework". They might even deliberately try to stay away from each other's structure. In other words, it can get really really weird.
I would like to answer from a humble listener point of view, with absolutely no music theory background. For me free jazz is like an open window into musician's mind. It's his stream of consciousness rendered in real time into music. If you can tune to this transmission (and the only thing I believe is required to do this is to be completely calm and relaxed) you might be even able to read his/her emotions, thoughts maybe? Unless we develop some machines to read other person's mind, free jazz is the only medium to achieve it.
But, you know. It might be just completely different. I've read somewhere an anecdote about one musician asking another how does one play jazz. "Oh, just play off-key, but stay in the groove!", answered the old musician. "And how do I play free jazz?", the younger wanted to know. "Oh, then just f*k the groove!".
In some ways free jazz can be easier to understand than other jazz forms. You really don't need music theory since the central theme of the genre is to free the performers from exactly the conventions that music theory analyzes.
Sometimes that means freedom from traditional song forms. Such as the common structure of bebop having a familiar "head" followed by a succession of solos, usually returning to the head at the end. Free jazz often ditches the idea of song form altogether, often having the players soloing simultaneously.
Sometimes they seem to be freeing the forms from their traditional constraints. Coltrane's "Ascension" for example used a single short line to create, basically, a 'non-head' where all musicians take that line and go where they want for a certain period. Then they move onto solos, each separated by a return to the "head." They are not limited to measures or even a specific rhythm or beat. They are free to go on as long as they feel. Except for that one very short phrase it is 100% improvisation.
One thing they almost always free themselves from is harmonic structure. Whereas previous jazz had increasingly complex chord structures which are heavily entrenched in music theory concepts like cadences and resolution, free jazz ditched the constraints of chord structure completely. Many free jazz groups lacked any polyphonic instruments such as piano or guitar. For most jazz pianists chord progressions and the interplay between each chord is their stock in trade. This creates a structure which would limit where the soloists can go with their melody. To avoid this they just leave out piano completely.
Far from needing a music theory background to "understand" the music, the goal was to free the performers from those type of restraints. When listening to free jazz you are to focus on the expression of the players - less emphasis on what they're playing and more on how they are playing it.
It can seem that understanding free jazz is difficult, but to me the real challenge was getting past the harsh and often cacophonous sound that results from removing the structures we are used to hearing. It requires letting go of your expectations and listening to the performances.