I have heard styles of magic being compared to genres of music. Is there indie magic?

Indie magicians are my solace in a sea of scenester scum.

https://www.urbandictionary.com/define.php?term=Indie%20Kid

I think indie is hard to define but yes I think so. least I have seen some, what would call, off the wall performances.

Could you name any?

Well, naked ladies spring to mind. https://www.youtube.com/results?search_query=naked+magician

Ursula Martinez is a performance artist, not really a magician. She's frequently lumped in because of that one video but I don't think she really does any other magic stuff.

If magicians are not really performance artists, then perhaps they are really indie charlatans.

Most who perform as something other than the "classic anodyne" entertainer had to find their own characters. Max Maven, Teller, and Johnny Thompson are easy examples. Some others who come to mind in no particular order include Flip Hallema, Peter Samuelson, John Carney as Mister Mysto, Juan Tamariz, and Luis Piedrahita.

Rectangles and squares.

The anodyne necklace, as they say, has the power to relieve pain. There are occult beliefs that the hangman's noose possesses mystical powers. Rope tricks spring to mind and perhaps doing such while dressed up as an executioner on a scaffold would be a bit indie, or perhaps just a bit morbid.

Some card guys are called underground: fellows who essentially perform for an elite audience and I guess one might say they are a bit indie - if that is what it means.

Underground, as was the card table where Braue took notes? That's different from publishing legacy material.

So, about the storytellers and real magii out pretending to use trickery?

I don't believe that indie is a musical style or genre. It's more of a marketing style or business model.