I find my dad's behavior disgusting after finding out he had a new gf a month after my mom's death.
How long should he have waited?
He was once with my mom for 20 years, that's not the point though.
It can be disrespectful to replace a partner so quickly after their death, and people are usually expected to take some time to grieve.  However, you father has made his own decision, and you should respect it.  You have nothing to gain by calling him names.
I don't respect him. He just wants to have fun. It's fine though, I have to move on, but that doesn't mean there can't be some drama here.
That's your decision and it doesn't mean you have to like his new relationship.