The Labour leader confronted Mr Johnson in a heated Prime Minister’s Questions on Wednesday and claimed he was giving racism the "green light".
It came in a confrontation that saw the Prime Minister promise to ban people guilty of sending racist abuse to footballers from attending matches.
Mr Johnson said the UK Government was taking “practical steps” to ensure those responsible for the sort of abuse aimed at Marcus Rashford Jadon Sancho and Bukayo Saka would be barred from matches.
Speaking in the aftermath of the trio of England players being racially abused following the nation’s Euro 2020 final defeat to Italy, Sir Keir demanded answers over Mr Johnson’s lack of support for taking a knee.
He said: “We could all see what’s happened here – the government has been trying to stoke a culture war and they’ve realised they’re on the wrong side, and now they’re hoping nobody has noticed.
“Why else would a Conservative MP boast that he’s not watching his own team?
"Why else would another Conservative MP say that Marcus Rashford spends too much time playing politics when he’s actually trying to feed children that the government won’t?
"And why will the Prime Minister refuse time and time again – even now – to condemn those who boo our players for standing up against racism?”
Mr Johnson insisted the UK Government was taking practical steps to ban racists from football.
He said: “We stick up for them and what we’re doing is taking practical steps to fight racism – changing the football banning regime, fining the online companies, and we will use more legislation if we have to – just as we used the threat of legislation to stop the European Super League.
“I don’t want to engage in a political culture war of any kind, I want to get on with delivering for the people of this country.”
Sir Keir then challenged Mr Johnson over his own comments and claimed the problem of racism was rife throughout the Conservative party.
He continued: “On 7 June the Prime Minister’s spokesperson said this: ‘On taking the knee specifically, the Prime Minister is more focused on actions rather than gestures’.
"On 14 June, the home secretary said ‘I just don’t support people participating in that type of gesture politics’.
“So there’s no point pretending that these things weren’t said.
“The England footballer Tyrone Mings … he said this labelling anti-racism messages as gesture politics served to stoke the fire of racism and hatred – Prime Minister they’re powerful words from someone who has himself been subjected to racist abuse. He’s right, isn’t he?
“Football’s a game, racism isn’t, Prime Minister. That’s why many of us have been involved in the charity Show Racism the Red Card for years. But far from giving racism the red card, the Prime Minister gave it the green light."
Mr Johnson replied: “I want to reiterate my support, our support, our total support for our fantastic team and I support them in the way that they show solidarity with their friends who face racism.
“The home secretary has faced racism and prejudice all her career of a kind that he can never imagine, and she has taken practical steps to get black and minority officers into the police in record numbers.”
A 37-year-old man has been arrested by Greater Manchester Police over social media posts directed at England players.
An online petition calling for the FA and the UK Government to ban those who have carried out racist abuse from football grounds for life has reached more than one million signatures.
Earlier, former minister Steve Baker said the subsequent outpouring of support for the players who were subjected to abuse following the penalty shoot-out with Italy should serve as a “wake-up” for the Conservative Party.
Mr Baker warned the Conservatives needed to realise “just how powerful our words are” when addressing issues such as racism and taking the knee.
“We have to get alongside those players who are taking the knee and understand they are not saying defund the police, they are not anti-capitalist,” he told BBC Radio 4’s Today programme.
“What they are doing is saying ‘we suffer racism’.
“What I am saying to my colleagues is that we have to confront the reality of how we are sometimes heard, even by people on our own side.”
Downing Street said they would seek to introduce the changes to the football banning regime through the coming Online Safety Bill following a “swift” 12-week consultation period.
“We will want to introduce it as quickly as possible working with the FA, working with social media companies and others,” the Prime Minister’s official spokesman said.
Banning orders are issued when someone is convicted of a “relevant offence” linked to a match, including crimes such as disorderly behaviour, making threats against people or property, and possession of weapons or alcohol.
The list also covers crimes set out under the Football (Offences) Act 1991, which include racist chanting, pitch invasion and throwing missiles.
The duration of a banning order, which is used to bar individuals from attending matches and in some cases can require them to surrender their passports ahead of overseas fixtures, can range from a minimum of three years up to a maximum of ten years.