According to it, we should first turn off the camera before turning auto-focus on/off. That's quite cumbersome obviously.

That seems pretty ridiculous. Perhaps the authors are serious about their target audience being dummies.

I am confused if this might harm my camera or lens in any way?

You won't hurt anything. It's fine to turn AF on or off while the camera is turned on.

For evidence, see page 170 of the T5i manual (PDF), which covers manual focus operation. Note that it instructs you to switch the lens to MF but doesn't mention turning off the camera first.

As Rob points out in another answer, you should probably avoid changing the focus mode switch while the lens is actually autofocusing, as it would be if you keep the shutter release half-pressed or set the camera to Continuous AF mode for shooting video. So don't do that. Changing the focussing mode or other settings during use seems like a strange and unlikely thing to do, though, and it seems unlikely that you'd find yourself tempted to do it.