> Your first example based on income is also grouping of individuals, exactly what you criticize in the second part.
No, not on some kind of identity. There is no "makes less than X" group, anyone can be a part of that group and anyone in that group can stop being a part of it. That's not true for gender, ethnicity, political convictions etc.
> It is to find out how we can lift everyone to have the same chances at the beginning, taking structural and unconscious factors into account.
Take everyone's children away from their parents, make the state raise them. If you want to exclude the parents' culture and values and the peer group of children from having influence on their future, that's the way. It's not a particularly nice thing, and I doubt that many people want it though.
> One could even say that the income base lines for eligibility in social programs can be seen as arbitrary as well.
Absolutely, they are. But they are the same for all, gender and ethnicity don't play a role. The SJW-alternative is having different laws for different people "to right a historic wrong". Which is pretty much incompatible with anything that wants to call itself democracy.