I opened a secured credit card with Wells Fargo about a month ago. The personal banker asked me if I was a permanent resident and I told him no. But he said that unless that he checked that box I would not qualify for a credit card, even a secured credit card.
So I told him to and he did. I now have a credit card and I am working towards building a credit history. I would point out three things from my experience that I want you to consider.
First, your SSN# is for life and so building credit with it is a must. Second, the categories the bank uses were made before DACA. Finally, I assume you are trying to build credit from scratch in which case you are gonna start with a secured credit card using your own money as a deposit.
In short, I am not what you might call a dare devil but I am not losing any sleep over this. I am now building a credit history and I don't see why the bank would sue me for trying to "defraud" it. Hell, I know many people with multiple credit cards who don't even have DACA.