Oh, FFS. Coronaviruses mutate all the time, and have been doing so since long before anyone even knew what a virus was. Until the recent hysteria, though, nobody cared if there was a new cold going around.
Exactly. Our natural immune systems aren't that discriminating. However an individual's own immune system might handle original strain "A," it'll similarly handle variant "B," "C," and "D," etc., etc.
It is possible that the same may not be true for those vaccinated against a narrow portion of the spike protein associated with original strain "A"," but that isn't my concern.