Hi JW:
Yes. This is a difficult decision and I was faced with the same dilemma with both of my religious-faith-believing parents. However, as with the case of my father, he told me that he is too old to change his mind (at age 72) before he died at age 73. Up until his death he continued to attend Catholic mass and spent many hours praying because he knew he was dying, and so did I know he was dying. So, instead of "insisting" that he believe what I believe, I knew that my days with my father were shortly numbered. Therefore, I decided that if I were to "expect" that he might have changed his belief's, then the least I could do is meet him half way... that being said, I chose to attend Catholic mass with him so he was not alone, even when I am an Atheist. In the last year that I spent with my father, it meant more to him that I spent time with him in "his world" than it ever would have had he changed his beliefs. I have absolutely no regrets of attending Catholic mass with my father over those final months of his life. It meant a lot to him. I got something out of it, too, although not on a superstitious spiritual level.
However, that is a rather unusual situation in that, he was 72/73 and was dying. I'm sure you understand.
Now, as for my mother, she has purchased me books such as, "The Purpose Driven Life" and enthusiastically encouraged me to read it. Well, I politely explained to her that it does not hold any value of purpose for me to read it in the same way it hold value, meaning and purpose for her. I still have the book sitting on my bookshelf... right beside my "The God Delusion" book, written by Richard Dawkins.
Had my father changed his mind, or my mother for that matter, there certainly would have been the chance that a schism would have occurred. Such a change can cause enough emotional instability to the point of shaking loose their fundamental identity to dangerous levels of depression or even suicidal ideation. The key is to replace the void with a new understanding so that is is liberating rather than threatening.
However, who is it that has the right to introduce them to this new insight?
No one.
Unless they ask or seek for that insight on their own, it then becomes a matter of teaching. But to proselytize any subject to anyone without their formal approval is unconscionable, UNLESS their beliefs have a direct effect on your health and well being, as in, causing you or anyone else harm. Then anyone has he right to address the cause of that harm... such as proselytizing, in and of itself, for example.
If the discussion of your Atheistic views ever comes up by the approach of either one of your parents, then you certainly have every right to begin the teaching process. I'm sure it is safe to assume that your parents already know that you are an Atheist. If not, then whenever they decide to approach you with something that is religiously slanted, you also have the right, then, to disclose your Atheist point of view as to why you no longer espouse their point of view, albeit your disclosure may come as a shock to them.
In closing, human's are usually motivated to do something in an effort to get their own needs met. In almost all instances, when we do something there is a personal self-motivated reason for it. In your case it might be that you would like to disclose to your parents your Atheistic views in an attempt to relieve yourself of your own fear of rejection, or to relieve yourself from possible future confrontations, or to get approval and acceptance from your parents, or to aleviate them from teir own ignorance and help them to achieve a higher level of rational thought... which would raise your self-esteem knowing that you are partially their "caregiver."
These are all normal human responses and needs. All humans have needs. However, what personal motivations drive us to meet our own needs can often be very obscure. I am "guilty" of it, too. But, that is what being human is all about. The key is to realize and understand what and why you are trying to get a specific need met, and to question weather there is a legitimate need there, or if it is something that can be met in another way, or by someone else... like baking cookies for your parents, instead. (That was not meant to be condescending. It was an example short of a better one to use).
I hope this response has helped you in some way. I am trying to get a need met by answereing your question. I need to my ego filled by having others believe that I am a know-it-all. It has nothing to do with actually helping you at all. ...just kidding. :) ...but do you see what I mean, I'm sure.