it depends on whether the jury buys your story, can you prove to them you are sincerely ignorant and acted in good faith? Or will they think you're playing dumb because you don't want to pay? Keep in mind, ignorance can only go so far, if you are put on notice, and warned (and you get that more than enough times when you get to court), it's going to be less convincing. Because the jury will ask "Ok, so you INITIALLY didn't know, but you were warned many times before you were brought here, so why didn't you give up and comply?"
Do you think a jury that pays or overpays their taxes are going to take nicely somebody who claims he believes he's immune for taxation?
You are correct that prosecution has the burden of proof on the crime, but when YOU are the defendent making the extraordinary argument of "not willful" "good faith" "ignorance", the burden of proof shifts to you. I don't work for the IRS (or any part of the government), I just know a bit about evaders because I read both sides and hate to be in their shoes.
You are not criminal for what you think, you ARE criminal if you lie, especially if you intentionally lied to escape liability of a crime. It's not thought crime, it's crime of perjury. But all of this goes out the window if you can convince the jury you're innocent, so go ahead.
By the way, if you can prove your actual belief that you are immune from taxation, that at most gets you off for "willful failure", it does not relieve you from tax liability itself. So it's not thought crime, it's the act of not filing, and willful is just an add-on.