>> I never mention who my current employer is either
Why is this? It's typically the most relevant information to a new position, and usually trivial to determine without you volunteering it.
Don’t worry, Equifax takes care of that for us. Both who you’re currently working for, and your current salary. It’s a service it offers to HR departments across the US.
One time they thought I worked on staff at the local zoo. Seriously.
It would be a waste of effort for HR. They don't have time for that I don't think. They want to get to a number not do forensics on your background.
Suppose you are just finishing a Ph.D. and took a few years off. Suppose you took a year or two to do freelance or work 1099. Suppose you went abroad to work for a year or two to take of your dying parent. These are all things I have run into.
Edit: One more good one. I've known people who won a green lottery or married an American citizen they met abroad. Showed up in USA with lots of skills having made much less in Eastern Europe.
I usually politely sidestep the "what's your current salary?" with a "in rolling to accept at least x, but we can negotiate if both parties are satisfied and get to offers". If a recruiter insists, I tell them I have a personal rule to never disclose that. I think I have lost a single prospect, which likely was never real to begin with. Likely just fishing.
While I'm at it, I never mention who my current employer is either. I usually obscure it on my cv of I'm still employed. I also had a request recently to provide a scan of my passport on initial application, which i also declined.
Honestly, recruiters think they can ask for any and all personal information they want. If you have value, no one will drop you because of it.