Do I have to take my Jeep Wrangler soft top all the way off?

It depends if you have the patience to remove it completely. I usually just fold it back all the way but removing it completely does have its benefits. If you leave it folded back you won't need to tie it down; it won't get caught by the wind or anything. It's just up to you if you want to spend the time removing it completely. Happy jeeping!

You don't have to take it off. It will stay down just fine if you just fold it back. Although it looks a little neater if you pick up some cheap straps and wrap them around it, but they aren't necessary.

I had a bestTop on my '95 YJ, and a factory top before that; I bent both frames by doing exactly what you describe. The bent part, on the BestTop, was not noticeable, other than from the inside, but it did hurt the rigidity of the top because it would not attach properly. I absolutely recommend a hard top; they are actually easier to attach and remove, and cheaper over time. You can expect to get about 60,000 miles out of your top; that's what both of mine gave me.

Short answer: yes, take it all of the way off.