It seems to me that a company uses "cali" for "t-shirts, coffee mugs ectâ¦" and he wants to use "cali.com" for "t-shirts, coffee mugs ectâ¦" but the OP is trying to say that since cali is generic for California, he should be ok to use cali.com anyway he wishes...
So the answer would be yes, there is a problem with that. But then again, this is "only" a hypothetical situation.....