The thing that most people don't get about bigotry and assholery is that if you sort people into these generalized groups then most, if not all, groups are on the receiving as well as the giving end. Most people fall into multiple groups, and many have ancestry from multiple ethnic groups.
You wouldn't know from looking at me how much Welsh, Irish, Scandinavian, Spanish, Celt, etc, is in my ancestry - you wouldn't know that I'm descended from people that the English think of as inbred sheep-shaggers, as well as people that the Welsh think of as mindless, money driven imperialists... heck, most Americans wouldn't even know that they have that stereotype of each other. You wouldn't guess that I have to remind family members who pride themselves on their English side that they're talking about themselves when they vomit out the pejoratives directed at other Europeans or at lower classes.
The poor and the middle class think that the rich are posh toffs, who wallow in pools of money that they don't care to spend on anything but flamboyant displays of wealth; the rich and the middle class think that we, the poor, are a heaving mass of drunken, racist idiots who don't appreciate the politics and charities that they support for our alleged betterment; the rich think that the middle class are in the poor category, and the poor think that the middle class are in the rich category.
The white poor in the trailer parks of America are considered backwoods, inbred, unhealthy, drunken, bigoted wastes of oxygen; the black people in the poor communities are thought of as violent thugs with absent fathers, who's only redeeming feature is musical skill; the rich white people in the cities are looked down upon as fools who name their child Mystical Rosemarybush India Kyaytyryn and feign gluten allergies, while rotting their brains with abysmal vegan diets and obscenely priced lattes.
The straight cis "white" guy who you think is a disgusting, misogynistic cunt based solely on the fact that you're a feminist and he's a man who disagrees with you, is also half Mexican and only white passing, and is so used to people stereotyping him as a rapist and misogynist that your "feminism" is indistinguishable from racism.
The pretty white girl, who you think is a rich white "Stacey", who you think gets everything handed to her and couldn't possibly understand the loneliness that you feel, grew up in an abusive religious household and suffers from the very same mental health issues that make you feel like no woman could ever love you and like you must adopt the label of "incel" and rally against the ills of the world that disadvantaged you, so your anger at the cards that life has dealt you is indistinguishable from the garbage that fundamentalists forced on her throughout her childhood.
I've been a victim of police brutality and medical abuse because I'm trans and mentally ill, I've been called xenophobic and racial slurs and treated like I'm inferior because of where my ancestors were born, but because I'm a pale guy on the internet I got told that I had no right to speak about those experiences, and it was practically indistinguishable from the officers and medical staff making it very clear to me that they already had a cover story and nobody would believe me.
When you sort people into these boxes, and actually follow every thread between them, you'll come to the conclusion that everybody hates each other, that everybody's victimized by something... but it's easier to pick out the instances that suit your own worldview, your own culture, your own experiences, and then assume that everybody you come into contact with on the internet can be sorted into the bad group or the good group.
What you're calling "intersectional" never seems to be about actually looking at every single one of those threads, seeing how they go in so many directions and affect everyone... it's just about expanding your "bad group" and "good group" to be based on more than sex/gender.
