The thesis of the illiberal left isn't that universality under the law shouldn't exist, the free speech shouldn't exist, that individualism shouldn't exist, that color-blindness shouldn't exist, that equality of opportunity shouldn't exist, or anything else.
The thesis is that those things don't exist in the real world. And it goes further than that, by saying that those things cannot exist in our society unless major changes happen. But the goal of abandoning liberalism is not actually to abandon those things, but to actually really realize them.
The thesis is that our current systems are not principled either in their means or their ends.
And it is true. Free speech is proportional to your means to challenge threats to your livelihood. Rule of law, universality under the law, equality of opportunity, simply do not exist - depending mainly on your socio-economic status but also on other axes such as racial perception of the individual by society, and so on.
Equally, the thesis isn't that we shouldn't have color-blindness, simply that the current social and material reality makes this impossible. As a result of this, attempts/pretensions at color-blindness simply make the problem worse.
If you didn't notice, the conclusion of the lefitst project after gender equality became progressive weakening and then almost abolition of gender - and I mean this in the strictest sociological sense of gender as the perception of a set of social attributes related to sex. The exact same set of theories are applied to race, before racial abolition there must be a realization of the existence of racial identity (which is indeed the definition of race in the leftist sense - racial identity is completely orthogonal to traits and genetics, it is indeed a completely cultural and social phenomenon and process), then true racial equality, then essentially complete racial abolition.
Systems that actually provide real equality of opportunity will always provide actually equitable collective outcomes on the average.
Equally, the leftist opposition is not to markets themselves. The leftist opposition is to our current set of property relations and to the relationships of productions. Attempts to change those when the time is not opportune have been disastrous, so the aim is to compensate and slowly work towards actually fixing them using state intervention that ancillary limit the freedom of the free market. But there is no inherent opposition to markets at all.
This worldview is only a few decades younger than classical liberalism itself, and started with the disappointed third estate of the French Revolution. Put simply, the thesis is that classical liberalism failed to achieve its promises of liberty, equality, and fraternity, and that making good on those promises requires more careful and less idealistic theories of society and social change than the idealist ones of classical liberalism.
I just thought you would enjoy not arguing against strawmen.