Everyone gets embarrassed when their parents go off their rocker -- but the rantings of Mel Gibson's father could create problems in his custody case ... at least that's what Oksana's lawyers want.
Sources tell TMZ ... during Mel's deposition today, lawyers for Oksana Grigorieva will dredge up statements made by Hutton Gibson during an interview back in August.
Among the pearls of wisdom from Hutton: "Half of the people there in the Vatican are queer." He also said he thought Pope Benedict XVI is a homosexual.
We're told Oksana's lawyers plan to paint a picture ... Lucia is at risk if she's around Mel's kooky dad.