Re: this sentence is correct?
This is perhaps the third thread in which you have started with "It is a controversial issue whether..."
This is not a natural.
It's also rarely a matter of "controversy" which carries a sense of disagreement with heated argument, not simply a matter of disagreement. If I want Chinese food for dinner and you want pizza, we disagree on our dinner plans, but there is no "controversy" in the common connotation of the word. In this very passage, you refer to "upsetting or controversial" problems.
Try starting as Bill suggested, or even more simply: People disagree on whether...
Last edited by Barb_D; 24-Oct-2012 at 18:26.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.