My assumption is they have news, and movies, and books, and holographic games....and Jedi have been around for how many centuries? They'd be featured in all kinds of media. And, they had all that before the Empire, which only formed a couple decades before the first movies.
I'm not really sure how this is even a discussion. The group has saved planets and societies for centuries. They'd be very well known. But clearly I'm not going to change my mind, and I'm not changing others....so I'm out on this part of the conversation.