How to disable mail preview popping up on right side on swipe in other apps

Are you pulling the multi tasking panel over ?

Swipe from right to left but not in the middle of the screen (vertical axis)

Or - I don't believe with iBooks it has to be a swipe from right hand side of screen, start swipe further in the screen middle

 

You mean the slide-over view opens? Unfortunately, there's no way to disable that, but you can switch it to open some other app other than mail, if there's something else that will annoy you less.

Here's an article explaining how to work with slide over.
http://www.imore.com/how-use-slide-over-multitasking-your-ipad

Btw, you don't have to swipe to turn the page in iBooks, tapping the edge of the page should do it.

 

As others have pointed out. Mail is opening for you because you're activating Slide Over. Which is part of the new iPad multitasking features. Simple just don't initiate the swipe from the edge of the screen or as Night Spring said, you can also just tap the right side to go to the next page. A swipe is not needed.

 

It happens to me sometimes and the slide over is a nuisance when you did not intend it.

But worried about the app opening in the background? Unless you force closed it it probably is anyway and who cares if it is? Not tying up that much system resource.