Man, I used to brush off stuff like this as no big deal. I figured a handshake is a handshake and people would just get that I meant well. Then I read up on it and realized the left hand is seen as unclean in a lot of West African and Middle Eastern cultures, so offering it can come off as a real insult. That changed my whole view, because it's not about being pc, it's just about not accidentally disrespecting someone at their own dinner table. Your coworker basically saved you from a super awkward moment in front of a client. I always go right hand now no matter what, even if it feels weird at first.