To make your pure CSS tabs functional on iPad, add
onclick="" to each label.
Yes, an empty onclick attribute. See this for reference: http://codepen.io/ryanseddon/pen/AExbc.
It’s a commun bug on iOS, but this little trick should fix it.
The other CSS solution to fix it is to put radio inputs on top of labels, with the same size as labels and opacity 0. This way, you don’t click on labels, but directly on invisible inputs.