My dad is a bigot as well, but he hides behind the hypocrisy that is his "Christianity" by saying that God didn't make anybody gay or trans, and that we're all just as screwed up as child molesters and murderers and rapists, so yeah... We're contributing to the spiritual and moral downfall of America apparently. So, I get where you're coming from.
Still, I'm so sorry to hear it though.

Don't feel that your actions would alter your father's feelings toward your sister and her husband, unless he plays the card of, "did you know about this?" or "do you agree with this?" on them. That might put them in a sticky situation I suppose. Still, it's not like they're going to (or would need to) stand against him on this topic, they're not the ones making this choice, you are.
It's a tough situation for sure, easy enough for you, but I can understand the hesitancy to possibly hurt your sister's situation. Even still, the choice to face your situation head on should never be seen as "wrong". All you're seeking to do is help yourself cope with the hand you've been dealt. You shouldn't force yourself to live in a misery derived from a medical condition just so that others can keep their heads in the sand and go on living life without a clue about something that may possibly make them angry or sad. Telling them may not be "fair" to them, but not telling them isn't "fair" to you. In the end, you are the master of your own life, nobody else.