Please note that your question is a little vague, so some of these might have slightly different meanings from the one you intended; I urge you to carefully read the definitions to ensure that the words are applicable to your context.
"Vulgarize," "popularize," "propagate," and many other synonyms would solve your problem. Note: if by "make accessible" you simply mean "to spread an idea," you can use all of these words (and many of their synonyms); if you mean "to make an idea less complicated so the masses can understand," I would use the first two. To "make [something] exoteric" would be to make it less complicated to teach it to the general public, so I tried to find words with that specific meaning (only "vulgarize" and "popularize" accomplish this—not "propagate").
The applicable definition of "vulgarize" (from HERE is: "make commonplace or less subtle or complex."
The applicable definition of "popularize" (from HERE is "make (something technical, scientific, or academic) accessible or interesting to the general public by presenting it in a readily understandable form."
The applicable definition of "propagate" (from HERE is "spread and promote (an idea, theory, etc.) widely."