If you read beyond the headlines or go to the website where you can read the full report and the datasets behind it, the report authors acknowledge that 'white working class' is a problematic term when it comes to defining a strata of society for statistical purposes, as is using FSM as an indicator of someone's class.
However, for the purposes of the report, in order to be able to create a dataset with clear parameters, they had to use FSM as a marker of disadvantage to align with the attainment data available from schools (as they track the achievement of students who receive FSM). They did also carry out more broad qualitative research that allowed them to gather views from people who did not receive FSM but who considered themselves white working class, though.
You can read all about the report data here: https://educationaloutcomes.org.uk/about/terms/
The report says nothing about white people being terrible parents, and neither does any news article I've read.
What the report does reveal are deep cultural reasons behind the lower educational attainment of white children living in situations of socio-economic disadvantage compared to their peers of different racial backgrounds.
This is a reality we need to be able to confront and discuss.
There is a culture of anti-intellectualism amidst benefit-dependent white British families, and a poverty of aspiration. Education is not seen as important. Children are not encouraged or supported to attend school regularly. Often homes are chaotic with minimal boundaries and parents are not supportive of sanctions for behaviour that are meted out by schools. When you have multigenerational families who are benefit dependent, this compounds the lack of support and aspiration for children. You can't be what you can't see. If no one you know has ever worked or gone to university, you don't see that as a possibility for you or for your child. It is very hard for individuals to break out of this pattern.
If you look at the report website, it's interesting that the research has all been done in either rural or former industrial communities, where multigenerational issues with lack of local work opportunities are endemic and lead to very little engagement with formal education. I think the results would look very different if our major cities were included.
As a teacher for many years, I've seen all this first hand. We all know the reasons behind the statistics - and the answer isn't to chuck more money at schools to fix it. You have to work with the community, to fix the culture, and what's going to fix the culture are opportunities for meaningful work in a variety of disciplines that are spread across the country rather than concentrated in cities. So many former industrial communities have had nothing invested in them since the mines or factories that supported them closed down a generation ago, and you've got children in these areas growing up in families where three or more generations have never worked. It's very hard to instil a good work ethic and love of learning in your children when you've never had it instilled in you, and when you think doing so will just give them false hope of a life you don't believe they'll ever be able to have.