*Returning “American Idol” producer Nigel Lythgoe managed to dis both Sarah Palin and her daughter Bristol in one fell swoop during his visit to “The View” on Thursday.

Lythgoe, a veteran dancer and executive producer/judge on Fox’s “So You Think You Can Dance,” was asked about a disparaging comment made by Sarah Palin regarding “American Idol.”

In her new book “America by Heart: Reflections on Family, Faith and Flag,” due in stores Thursday, Palin writes, “Did you ever wonder where the producers of ‘American Idol’ come up with the seemingly endless supply of people who can’t sing but are deluded enough to get in front of a national television audience and screech out a song anyway?”

Contestants on reality talent shows like “Idol,’ she writes, are victims of “the cult of self-esteem. No one they have encountered in their lives—from their parents to their teachers to their president—wanted them to feel bad by hearing the truth.”

After “View” co-host Sherri Shepherd read Lythgoe the quote [see photo above], he responded with this…

“I don’t know why she’s referenced the president. I think he’s probably got a bit more on his hands to worry about than ‘American Idol’ contestants. And I guess she wrote that before her own daughter showed her somewhat lack of talent as a dancer on ‘Dancing With the Stars.’” [Watch below.]

In related news, TMZ is reporting that the man who was attacked on Facebook this week by Willow and Bristol Palin says he does not accept their apology.

TMZ spoke with “Tre” — the person whom Willow called a “f**got”  after he criticized “Sarah Palin’s Alaska” on his Facebook page.

Tre — who tells us he’s not gay — claims he was offended by the comments and felt bullied by both women … saying, “Willow called me a f**got in front of the whole world and my family.”

When asked if he thought Willow was a homophobe, Tre replied, “I think she might be … She says ‘queer’ and ‘gay’ so much … so probably … maybe.”

Although Bristol issued a public apology through Facebook on behalf of her and Willow — Tre says he’s yet to hear from either one of them. We asked Tre if he accepted the online apology and he told us, “No way … Maybe if it was sincere and honest from them straight to me, I would consider. But it would have to be direct.”

Tre concluded, “People are saying these are baby grizzlies defending Mama Bear … but how is she defending her family by calling us queers and low-lifes and f**gots?