Irreverence is easier than holiness. Being an iconoclast is not without value, per se, but too often, being iconoclastic is the goal, and not the pursuit of truth. Tossing out as many traditions as possible is OK if the end result intended is baring out the simplistic form of what matters most.
I see this in church life. Too often, those motivated to do so are wrought of real disenfranchisement (racial/economic injustice, not as pretty/skilled/quick witted as their peers, or just sitting with a chip on their shoulder), not a deeply held passion that something broken needs fixing. They may come across as prophetic, or 'rebellious for the Lord', or as jerks.
Living a life that's true means living counter-culturally. If your life happens to coincide with the popular mode, great. If not, still live the way that Christ would have. And when you don't, stop, have at it, and get back into it. Easier said than done? Oh yeah. Bigtime.
Martin Luther's goal was not to destroy, but to reform. He was a true iconoclast. Accidental iconoclasts like Hudson Taylor just do their thing as they chase God's will, and what comes out is not irreverence, but holiness. In a more modern sense, Keith Green too. Maybe even Billy Graham. He could have lived hugely off of book royalties, but lived an average life financially. Compare him to Benny Hinn, who is making a fortune, and I know which life I would rather known for living.
Be a rebel with a cause.