You do make a point, but you used the wrong examples. All those words you site are synonyms for American words. The British person would be pronouncing them correctly, whether or not the caller had the vocabulary to know what the words meant.
On the other hand, to pronounce “axe” when the word is spelled “ask” indicates that the speaker does not know the “proper” pronunciation. This indicates that there may be a lack of education. I’m not aware of any black schools that teach a different pronunciation of the letters in the English alphabet. I assume she would spell the word as a-s-k.
Your example is about using different words when it should have been about accents. So, the question really is whether it would be a problem if the receptionist said tomaato instead of tomato.
Perhaps Tom would have the same problem with a white receptionist that said “y’all”, so let’s not be so sure he is racist yet. Maybe it is classism on the part of his clients that he is catering to, not racism.
I have a close black friend who is a partner in a prestigious law firm that is predominately black-owned. At that firm, I assure you, any receptionist who pronounced the word ask as axe would not have been given the chance Tom gave his receptionist. The standard for professional English is extremely high there, in part because of racist expectations. But, when I’m having a few beers with him, we can still talk like we did when we were growing up.