Sam Wilson: Found a place in Brookyln yet?
Steve Rogers/Captain America: I don't think I can afford a place in Brooklyn.
NYC is a very in-demand market, with many apartment-seekers being out-of-state dreamers, or local residents who have realistically been priced out of their own town by gentrification. This demand overloads landlords - ties up a lot of their time. Landlords need to efficiently screen out the unqualified, and "too low wage" and "too low credit score" are probably the #1 and #2 causes of rejection.
Is it unreasonable to collect salary and FICO Score? No.
Here's the thing. "PII" requires "Personal". Consider the following data:
Steve $95,000 720 June 1
Is this PII? No, it's not, because it doesn't definitely connect to a person. There are probably 100,000 Steve's in the NYC area, this doesn't say which one that is. Nor is there a viable path to misusing this data. It wouldn't be a data breach, because it's not connected with an identity.
If you don't want them having that data about you, then don't give them You - just let yourself be "Steve".
They would then proceed on the basis that they are willing to rent to any random person whose nickname is "Steve", on the basis that they make $95,000 and have a 720 credit score and want to rent on 6/1/21. After meeting you, their decision is made (so long as your facts actually do check out. Obviously if a credit check pulls a 380 score, then the deal is off.)
So if "Steve" likes the place also, then there's a meeting of the minds and now it's time: "Steve" discloses "My proper name is Samuel Thornton Hoppledinger GC, social 100-00-1234, employer is Acme Wing Nuts" etc. They run Steve's credit, checks out, rented.
They don't even need to retain that data
No need to even retain
Steve $95,000 720 June 1
All you really need is
Steve Claims Good Credit June 1
And you don't even need to retain that. As long you have good processes, all you need to do is pre-check their qualifications to even enter the sales funnel. Now you only need to record
Steve June 1
and the mere presence on that list implies qualification. And that's not sensitive at all, even if merged with email, phone and other identifiable data.
Now, circle that back 'round to your experience.
An aside: common scams
Now, some landlords run a scam where they charge you $30 to run your credit, but don't actually run your credit and simply pocket the $30. Those landlords will want all your details, solely because they need to maintain the pretense that they will run your credit. They are unlikely to misuse your PII for other purposes, but you never know - least, someone else may fish it out of the trash can they threw your application in.
You are also talking to real estate agents not direct landlords, and obviously the agent is trying to place you in agency relationship with themselves, either to charge you a fee for finding you a home, or because they have agreements with select landlords to be paid a fee when they place a reliable tenant. In which case they will only show you certain properties where that agreement exists.
Another scam is trying to get you to sign an agency agreement, which is that they are your sole agent for your search, and you agree to pay them (if the landlord doesn't) even if you find a place on your own without their help. This is always bad news and the answer is "hell no".