There's some who self identify with it, Skepchick and The Dixie Chicks come to mind, but it can be considered somewhat derogatory, dismissive, or at least belittling in some contexts to some people.

I think context and age matters a lot here (as well as personal preference) - young women and (especially) girls may use the term amongst themselves but middle age women almost certainly wouldn't, if you called your boss "chick," it would be seen as inappropriate, belittling and disrespectful. It's in the same category (but not "severity") as other diminutives like sweetie, honey, babe, girl, girly, and doll.

It may vary by region too, I know at least certain diminutives don't have the same connotations in the American South as they do elsewhere.

In general, you should probably avoid calling an adult woman you are personally unfamiliar with "chick" in many contexts, not necessarily because "PC police," but because it's just bad for communication - its not necessary and it can be a distraction from the actual message you're conveying.

Personally, as a woman approaching 40, I can't think of any context I'd care to be called "chick" in. Not necessarily offended but it would be just icky.

EDIT:

Some discussion:

https://english.stackexchange.com/questions/19098/how-deroga...

https://www.theguardian.com/commentisfree/2016/sep/30/bird-i...