At least the controversy about string theory has been in the public eye for a while now. It seems like physics hit the worst of it in the 90s and the public trust we have now is relatively sturdy.
The public trusts most areas of physics because we use them to build many artifacts, some quite amazing, we interact with everyday and also because there are solid experiments that repeatedly confirm them. Some may extend this trust to the most modern areas yet without experimental confirmations, but not everyone does.
The situation is quite different for many softer sciences for which neither of the above conditions is true. If the public found out they have been misled by a whole field for decades, the trust in that field could be shaken to a great extent. Even adjacent fields could be affected as collateral damage.
The situation is quite different for many softer sciences for which neither of the above conditions is true. If the public found out they have been misled by a whole field for decades, the trust in that field could be shaken to a great extent. Even adjacent fields could be affected as collateral damage.