The Jaws star, 76, has made headlines for apparently launching into a rant about transgender children and diversity on Saturday during a ticketed screening of the 1975 shark-attack horror at the Cabot theatre in Beverly, Massachusetts.
His boy Ben Dreyfuss, 37, has addressed social media accounts of his dad's alleged outburst by saying on X: "Wow, just looked at my phone and learned about the disgusting outrageous behaviour of one of my relatives."
He also joked: "Well, now you know why I refused to give him the password to his own Twitter account for a decade lol."
Ben added: "This will be my only statement on the matter. Thank you."
Dreyfuss had Ben with his 75-year-old screenwriter ex-wife Jeramie Rain.
Video of the actor's full remarks from Saturday has not been released, but attendees at the event have attacked him on social media.
One guest said on Facebook: "We walked out of his interview tonight along with hundred of others because of his racist homophobic misogynistic rant."
An X user claimed her girlfriend's parents attended Dreyfuss' event and attached a screenshot of a text message from one of them that said: "Went off the rails talking about how Barbra Streisand is a genius but he didn't listen to her because she is a woman and women shouldn't have that power.
"Then started sharing his views on the me too movement and started down the road on how you shouldn't be listening to some 10-year-old who says they want to be a boy instead of a girl."
And another X user claimed Dreyfuss said at the weekend event "women shouldn't have any power" and should stay "quiet" and "meek".
They added: "When asked about the #MeToo movement he said 'those people make me want to vomit' and that he didn't want to listen to eight-year-olds saying that they were born in the wrong body."
The Cabot theatre has issued an apology for Dreyfuss' "distressing" remarks, adding in an emailed statement to attendees: "We deeply regret that Mr Dreyfuss's comments during the event were not in line with the values of inclusivity and respect that we uphold at the Cabot.
"We understand that his remarks were distressing and offence to many of our community members, and for that, we sincerely apologise."
The theatre also told The Hollywood Reporter it was "aware of, and shares serious concerns following the recent event with Richard Dreyfuss".
It added: "The views expressed by Mr Dreyfuss do not reflect the values of inclusivity and respect that we uphold as an organisation.
"We deeply regret the distress that this has caused to many of our patrons."
Dreyfuss has not yet publicly addressed the controversy.
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