Bridges said he was suspicious that what we were seeing in NZ was "control freakery". He said banning people from speaking was going against history.
"Let New Zealanders decide for themselves about what they want to hear."
He likened the bans to "rule of the mob" where people were shouted down.
"Let's leave that to the Americans.
"You might not like Don Brash, you might think he's boring, but everyone has a right to free speech."
Brash was scheduled to speak to students about his political career on Tuesday as part of the same series of talks.
Thomas made the decision to cancel the event after threats were made on social media as discussion about free speech heats up in New Zealand.
Brash was part of the group that raised money to challenge the decision by Auckland Mayor Phil Goff to ban controversial right-wing Canadian speakers Lauren Southern and Stefan Molyneux from holding their event in a council venue.
Their pair's event was called off after the owners of the Powerstation, a private venue they had booked, pulled out at the last minute.