Well, I've been told to go and educate myself by several strangers on the internet upthread. (Must be cold up there, on the moral high ground).
So I did. And I want to modify my position. I think context and intent matters too. Racism is not actually an offence on its own. In cases of employment discrimination, or discrimination by an organisation against a service user or member of the public, the details are specified by the Equality Act 2010, which defines the offence of harassment. There are 9 protected characteristics, and race is one of them. Separately, if a crime has been committed, then it is also possible for that crime to be a hate crime if it was motivated by hostility towards one of 5 characteristics, and race is one of them.
I don't think what the OP described constitutes a crime, therefore it cannot be a hate crime. The test for harassment then is for a persistent and deliberate course of unreasonable and oppressive conduct, targeted at another person, which is calculated to and does cause that person alarm, fear or distress. That's quite a stiff test ... and the key term there is "is calculated to and does cause ..."
For the comment referred to by the OP to constitute harassment, it would be necessary to show that the poster's intent was to cause harm, and that harm was indeed caused. And for that to have been unreasonable. That is patently not proven on the evidence adduced by the OP. Therefore ... it does not meet the standard for harassment. (Never mind the more immediate legal issue, that there appears to be no employment relationship in this situation, or any other legal duty owed by the poster to the recipient).
Interestingly ... if the poster had been a pub landlord and had ejected the target of the comment from their pub with the same commentary, then it would be harassment on grounds of race, capable of being brought to a civil court. The usual compensation payout is about £10k. There was a case involving travellers that was published recently on exactly that basis.
But, in summary ... back to the OP and the many angry social justice warriors on the thread ... I have read up on racism, and this is still not racist.