It's as though you're pretending not to know that the word racism both (i) has a pre-existing meaning and (ii) is morally charged.

The pre-existing meaning of the word is that racism is a property of beliefs and attitudes and ideas that a person might have. [For instance, beliefs that a particular race is superior in some sense (e.g. morally) or that another race (which may or may not be inferior in some way (e.g. morally)) needs to be kept down / treated with hatred or aggression or contempt. Also, there is the attitude of being overly eager to explain and judge others' behaviour in terms of racial characteristics.] A person in whom those attitudes have taken root and exert significant influence over their behaviour, is what we call "a racist". This usage is secondary to the first - we only call someone a racist because of the racist attitudes etc. that they hold. Similarly, it might be that an entire institution embodies or acts on the basis of racist ideas, and in that case we can legitimately talk about "systemic" or "institutional" racism. (Here we might think of laws that discriminate between races, whether explicitly or in the 'disparate impact' sense. Or we might think of a police department that unfairly profiles suspects as being of a particular race.) Again, the ideas/attitudes are what is racist, and the institution is called 'racist' solely because those ideas have 'taken root' in some sense.

Now, the concept "racism" that I've explained above, which you knew perfectly well even though you were pretending it meant something else, isn't used only in disinterested, academic contexts for describing and explaining reality - it's also used in everyday life where to be a 'racist' is to have transgressed against current social norms, such that one loses status and is shunned.

Where the rubber meets the road is that if person A says something racist (in the sense I outlined above) then (1) they are labelled 'a racist' and then (2) they are cast out of polite society. The people whose agenda you are serving want to bring about (or rather to justify, now that it already exists) a bizarre, Orwellian state of affairs where espousing racist ideas leads to greater or lesser stigma depending on the race of the person doing it, as opposed to the ugliness or dangerousness of the ideas themselves. They do this, rather cleverly, by interfering at step (1) rather than step (2) above.

This is what I want you to understand: that while, from an abstract perspective, the "symbolic representations" are arbitrary, the particular way that the "symbolic representations" have been meddled with in this case serves no purpose whatsoever besides the nefarious one I described in the previous paragraph.