Current salary information required for a onsite interview and offer

I am currently in the interviewing process with some well-known tech companies. One of these companies (mid-sized) told me today they would not let me continue to the onsite interview, or make me an o

I am currently in the interviewing process with some well-known tech companies. One of these companies (mid-sized) told me today they would not let me continue to the onsite interview, or make me an offer, without my current salary information. They also said they would verify my current salary during the background check process. Is this a common demand that will be required of me at most mid-sized and large companies? Should I just stop the interview process with this company? Note: I am currently being significantly underpaid as a contractor -- this is on purpose, as I signed up for a project to essentially take a break from burnout from full time work, and work very part time and for minimum wage. My previous salaries are closer to what is considered a normal salary for somebody with my experience. I am also interviewing with Big-4 companies (which I am currently only in the early stages). Will Big 4 companies also demand that I give them my current salary/pay information to proceed with an offer? I don't mind giving up my pay information to 3rd-party background check companies, since I don't want to lie. But I think my current pay information will allow everyone to completely lowball me since I am essentially being paid minimum wage (and also working free hours). Thanks for any advice. edit: grammar