Actor John Cusack went as far as to accuse DeGeneres of "normalising mass murderers" through association with Bush.
Liberal activist Peter Daou tweeted that he has "nothing in common with George W. Bush, who launched a war based on lies that caused untold carnage".
Another spectator asked: "Is my vision screwed up?"
Clinton Yates, a columnist with ESPN's The Undefeated, said the sight "definitely qualified as a Sunday shocker".
Some critics noted that Bush also lobbied for Supreme Court Justice Brett M. Kavanaugh, who faced multiple sexual misconduct allegations last year ahead of his confirmation. Kavanaugh has denied the allegations.
On Tuesday, DeGeneres addressed the pair's unlikely friendship and the criticism surrounding it on her daytime talk show.
DeGeneres explained that Charlotte Jones, daughter of Cowboys owner Jerry Jones, invited her and her wife, Portia DeRossi, to the game. They decided to go to "keep up with the Joneses," she joked.
During the game, the broadcast showed a shot of the two laughing, and "people were upset," the star said.
"They thought, 'Why is a gay Hollywood liberal sitting next to a conservative Republican president?" DeGeneres continued.
"A lot of people were mad. And they did what people do when they're mad: they tweet.
"Here's the thing. I'm friends with George Bush," she explained of the former president, who was previously a guest on her show in 2017.
"In fact, I'm friends with a lot of people who don't share the same beliefs that I have."
"We're all different and I think we've forgotten that that's OK that we're all different.
"For instance, I wish people wouldn't wear fur. I don't like it, but I'm friends with people who wear fur," the host continued, adding, "But just because I don't agree with someone on everything doesn't mean that I'm not going to be friends with them. When I say be kind to one another, I don't mean only the people that think the same way that you do. I mean be kind to everyone."
Her monologue clocked four million views on Twitter in an advanced release on social media before it even aired on television.
A spokesman for Bush told Fox News: "President and Mrs Bush really enjoyed being with Ellen and Portia (de Rossi) and appreciated Ellen's comments about respecting one another. They respect her."
The Advocate and Out magazine, both LGBT news organisations, published articles in response to the controversy that highlighted Mr Bush's push in 2004 for a constitutional amendment that would have prohibited marriage equality, The Washington Post reports. Several critics pointed out that the amendment was a wedge issue in the then-president's re-election campaign, contrasting his stance with DeGeneres's activism.
"As one of America's most visible (and powerful) queer celebrities, Ellen pal'ing around with those who have actively tried to harm us feels disappointing, irresponsible, and dangerous," Out magazine wrote.
