Question: Curious on why the surgical equipment doesn't melt when removing the Queen chest burster from Ripley when she has acidic blood?
Question: Why was Ripley cloned?
Answer: In Alien 3, Ripley discovers there was an Alien queen embryo growing inside her, so she chose to kill herself. By cloning her, scientist were hoping the Alien queen embryo she had in her at the time of her death would also become cloned, which finally happen after the 8th try. This is also why the Alien queen they extracted from Ripley has some human traits.
Answer: This is just speculation (and I haven't watched the movie for ages) but the operation is done with medical equipment in a facility designed for studying Aliens, which the military knows a little about. Maybe it is made of futuristic acid proof material.