Not too close? I agree with spacial, what you do will depend on what you want from them after.
mmm, you might be surprised by their reaction, you never know.
Well, I would suggest different strategies for dad and mum. A lot of dads like the facts. Give them the sciency stuff, what it may be caused by, what the science community says, what the psychologists classify things as.. For mum be more emotive - how it has made you feel, the pain of it. This is pretty stereotypical though, but might fit the ticket.
Things I think are good:
Not too much detail. "I've felt I was a man inside for a long time" - perfect I think, detail later.
Give examples of you that they may have noticed from you growing up i.e. it has been with your along time.
Talk about the alternatives to being you - i.e. suicide, mad depression, lack of function....
Talk about 'cures' i.e. none exist.
talk about why you are telling them
reasure that they did nothing wrong and it is not their fault
reasure that you will still be interested in things you did before (if true) i.e. you still want to be involved in cooking or fixing the car or the gardening etc...
Make it clear that it is not open for discussion, that you are telling them, not asking for opinions.
Hope this is helpful.
Best of luck!