Yes, but the social context of men and women in professional environments is different. Causal terms like this carry a lot more baggage for women, who have had to fight for decades to be taken seriously in the workplace. "Chick" is more likely to remind somebody of all the times they have been talked down to than "dude" is.

Obviously not everybody responds this way but we should be aware of the context.

Sure, in a professional environment both are inappropriate, perhaps "chick" even more so given the historic inequality in the workplace between sexes.

That said, I'm curious what is at all "professional" about the greater context that spawned this particular discussion in the first place.