Democratic activist Stephanie Keddy wrote: "I'm not angry about Vince Vaughn, just profoundly disappointed.
"I want nothing more to do with him. Once upon a time I found him quite entertaining. Not anymore."
Trump supporters appeared to welcome the exchange, and hit back at people suggesting he was now "cancelled."
A user tweeted: "The fact that people are outraged that Vince Vaughn shook his president's hand like a true red blooded American is laughable...news flash cupcakes, @realdonaldtrump IS your president too!"
Another said: "Who knew this handsome actor could be a trigger for all these snowflakes! Get over it!."
In an interview with GQ, Vaughn was outspoken about political issues and criticised the lack of gun control in America.
In October, Ellen DeGeneres was widely criticised when she was spotted sitting next to George W Bush at a football game. The President opposed same-sex marriage throughout his time in the oval office.
