You don't have to submit to any requests of a perspective employer. You can simply leave. You may not get the job though.
From the employer's perspective a lot of these things go to character. I know, I know, what people do in their personal lives is their business. Just for the record I do not drug test my employees. I just don't care what they do after hours as long as they are sober on the job. It would, however, save me 12% on my worker's comp.
But like this idiot running for mayor of NYC; it goes to character. Yeah yeah, it's his personal life, doesn't affect his job performance, yada yada. Except it does. I had a guy who came in to interview for a job as a mechanic. Nice guy, talked a good game, sounded like he knew what he was doing. He was 53. Seemed like he'd be a good fit. But then he went on to talk about never being able to retire because his 23 year old girlfriend was pregnant, on top of that she was going in to rehab... again. I did not hire him. See, the details of his personal life indicated that he makes poor personal decisions. As the owner of the business, I have spent years and risked literally everything to get this thing off the ground. I would be depending on him to do work according to my standards, often in my absence. Given his previous poor decisions I doubted his ability to do that. And as the guy assuming all the risk, that is my right. If you don't want to answer questions or provide information about your personal life to a perspective employer, don't. Feel free to do what they did. Go out and risk everything and start your own business. I doubt your perspective will be the same when you are putting your trust into someone who will not answer your questions.