I think everyone faces that question in their own time and their own way. I agree there are some situations where you need to apply caution, not everyone is all that enlightened. But to the people who matter to you, if you feel strongly they need to know you have a choice to make. Be aware that not all relationships survive it, but the ones who do can grow closer than you ever imagined. It's been said "Be true to yourself", just keep in mind everyone's truth is different.
Most of the people who genuinely love you will not give it a second thought, as they know YOU didn't change. Some no matter how close they are you may never tell. you have to learn how to accept that too, especially since you are making that judgement. Keep in mind that there will always be a certain level of "don't ask don't tell" involved in your life depending on what your chosen profession is, mainly because you can't always control the ones you are surrounded by in such settings. You CAN however construct your best and most rewarding personal life, you CAN choose your friends.
I suggest if you have a particularly close open minded friend, you start with them. It can really help to have at least one supportive person with no axe to grind to help you sort things out. For me it was my adoptive older sister. Good luck with your decisions, I wish you the best.