I'd never used the term before I met DP, but he calls me babe and I reciprocate. He also calls his DDs babe, I have been known to let it slip out when talking to my DCs too.
Where I did draw the line was hearing him call his ex babe on the phone
- that felt like a kick in the stomach. He has also used it while talking to female work colleagues in my presence, so I know he doesn't see it as being quite as personal as I do.
So while I accept that it's just a term of endearment, like darling or love or whatever, it is a bit too gushy for me to feel happy with him calling just anyone babe. However, his DDs are on the approved list.