This is a very personal thing. For some people (I would guess most people), it matters, and they -- at the very least -- present a different face when at work vs. out with friends. Many people have further stratification.
I do get what you mean, though. As I've gotten older, I've found that maintaining different personas is just exhausting and not really worth it. But I also don't have anything in my life that I'd be embarrassed about depending on audience, and I don't consider myself a member of any underrepresented groups or subcultures that the mainstream would consider "weird" or somehow undesirable. So it's easy for me, which isn't true for everyone else.
I am not sure about this, I used to think like that but the older I grow the less I care. I even embrace the fact to show the same persona everywhere.
I haven't been actively using FB for the past few years though but maybe this is something that newer generations have already concluded in.