Sun retained his 200 and 400 metres freestyle titles in Gwangju but his celebrations were soured when Australian rival Mack Horton and Briton Duncan Scott refused to shake his hand in separate podium snubs that left Sun furious.
Several swimmers, including Olympic champions Adam Peaty and Lilly King, have come out in support of Horton, beaten by Sun in the 400m final, and 200m bronze medallist Scott.
But Dressel on Wednesday sought to defuse a volatile situation, which had threatened to spiral out of control on Tuesday night when Sun angrily confronted Scott after the medals ceremony.
"One thing I learned from my older brothers is there's two sides to everything," said Dressel, who swept seven world titles in 2017.
"I understand why the Chinese fans could be upset - and I also understand where Duncan and Mack are coming from," he added.
"But it's a competitive sport and I think they should have the right to voice what they believe in. Kudos to them for doing that - and the Chinese are doing it back."
Horton was labelled a "clown" by China's state-run media for refusing to step up to the podium after taking silver in the 400m while online trolls posted death threats on the Australian's social media accounts.
"The Chinese are upset because people are protesting," said Dressel. "It goes both ways."
Horton and Scott were both given official rebukes by swimming's governing body FINA - as was Sun, who squared up to Scott and jabbed a finger in his face, barking: "You loser, I win!"
Peaty reiterated his support for Horton and Scott after retaining his 50m breaststroke title on Wednesday.
"It's free speech - and I don't think anyone should get a warning for free speech," said the seven-time world champion.
"Those dopers shouldn't be in the sport, there shouldn't be any doping in sport," added the 24-year-old.
"They just need to grow up or just stop doping really. But obviously it's going to be an uphill battle for athletes to get their rights and race clean athletes as well."
The bad blood between Horton and Sun dates back to the 2016 Rio Olympics where the Aussie called him a "drug cheat" over a prior three-month ban.
China's sporting idol has always argued that he took prescribed medication for a heart problem, while Chinese doping officials are believed to have failed to update their therapeutic use exemptions (TUE) list for athletes.
His latest brush with controversy comes after a leaked FINA doping panel report claimed Sun allowed blood vials to be smashed with a hammer after testers visited him last year.
"They're truly the most courageous guys and I couldn't be more proud of them," said Horton's countryman Mitch Larkin.
"They're standing for what they believe in and that's clean sport. If we didn't believe that we wouldn't be racing here today."