That's just plain nonsense if you stop and think about it because it isn't just manufacturing that has lost jobs. Hundreds of thousands of American jobs have been sent overseas in dozens of industries, both manufacturing or service. The overwhelming majority of those jobs were not unionized. The greatest enemy of industrialization is the fact that a worker in China makes a tiny fraction of what a worker in the U.S. does, unionized or non-unionized. You could have done away with unions decades ago and it wouldn't have saved many jobs.
My father who passed away this year worked in a factory for 38 years (machinist and aerospace workers). The plant made equipment for the medical fields. Six years ago they closed the plant doors for the final time. The union had for many years worked with the company trying to keep the plant viable. The union approached the company and asked what did they need to do to keep the doors open? The response was “even if we payed you minimum wage it does not make economical sense”. The plant was moved to Mexico.