How much music theory knowledge is required to compose music?

Technically speaking, very little music theory knowledge is “required” to compose music. Music theory is, essentially, what musicians have learned over the course of several hundred years about how to write music that is interesting and sounds good. In other words, music theory is there to help you, not hold you back. 

When you learn music theory, what often happens is that you expand your broader understanding of music, which can be a very helpful safety net. The more music theory you know, the easier you’ll be able to distinguish between the good ideas and the not-so-good. You need to know the rules before you can break them. You need to be able to write by the book before you throw the book away. If not, you run the risk of writing music that’s not nearly as clever as you think it is, that tries to be daring and experimental but ends up just being dull and vanilla. And frankly, I just don’t see the value in ignoring all the work that centuries worth of musicians have done into knowing how music works. Putting the time into learning and really understanding it can only make you a better musician and a better composer.

So, that’s my answer. Learn at least as much theory as you need to know to understand the rules you want to break.