My only real experience is a cousin who was terrified of telling his parents, and his brother, and us.
Once he'd told his brother, who was fine about it and told us, who were fine about it, and his parents, who were devastated, at first, but came to accept it and were helped by the fact that everyone else was fine about it, he felt like the weight of the whole world was off his shoulders.
He lives abroad, but his parents, who he was always really close to, especially his mother, visit him regularly and stay with him and his long-term partner.
If you are not close to your dad, them maybe your aim should be to move out first, maybe to a more open minded area, and then tell them, when you are ready.
Don't let it eat you up.