I'm on the opposite end of this spectrum.
I'm very sorry your cat got into the enclosure and very glad to hear no one got hurt in the process. With a nosy cat like that, keeping the dragon in a cat-free room or properly securing the enclosure will be the way to go, but I'd never tell you to get rid of your cat. That's not a decision of mine to make or even suggest.
I understand everyone here loves their dragons and they are like family, but remember cats can be like family to others, too. I would truthfully consider my cat my best friend - I saved her as a feral kitten in the woods (long story) and personally raised her since. If she ever did anything to hurt my dragons (though I don't like to refer to them this way, but are like my children to me), I would do anything to make the situation work, but not abandon my family/best friend.
I understand where everyone is coming from; cats are nature's perfect predator and a dragon is merely a play thing to them, but just like dragons they have their own personality. My cat may be a little ... b word... but she's no killer and completely trustworthy around my dragons. But this is me, not everyone.
Please approach your situation in the way that makes you and your animals safe and happy.