Capricorn would probably have the worst time because they are the most concerned for their public image. I think Scorpio would fare best.
The betrayal would sting Scorpio and the perpetrator would be amputated completely and permanently from the life. But I don’t think they’d be all that bothered over what came out. Because I don’t think you’d get at Scorpio’s actual dirty laundry. Their stained things, maybe. But their actual dirty laundry? Forget about it.
Pisces would also do well. Think “Elizabeth Taylor”. As if she cares what you think about her addictions or her love life. I don’t think so.
So what about you? Let’s say someone tells your secrets. What would you do? How would you cope?