Over the last 10 or so years, it has become more and more frequent that providers, unless you're finding them on backpage, will ask for references. The reasons are fairly obvious. Some of the providers and agencies are more, um, intrusive (for lack of a better word), then others but, aside from all the obvious reasons you can think of, there's one more that you might not have thought about: the lady has to feel comfortable with you. And each lady will have a different standard for what information she needs from you to feel comfortable alone in a hotel room with you, a stranger.
And, the screening process really is not that much worse than going on a date, is it? I mean most dates I've been on, I've been asked what I do, where I work, and many of the same questions that the providers and agencies ask. And I've been asked some of the same questions from women on dating sites.
Another little point: I'm not sure that any of the agencies, especially those that handle porn stars, keep the information they get from you anywhere except in their heads. Some might write it down in some little black book, but I don't think many of them keep any of the info online where it can be hacked or subpoenaed. Ok, I don't really know the inner workings of any of the agencies, this is a guess, but I'm pretty sure that the agencies I've dealt with over the last 10 or so years haven't kept the information.
In any event, If you really don't like the screening process, you can always use sites like date-check or similar sites. Although not every provider or agency will accept those sites either.