SEB (as most other card issuers) just rely on the credit report from UC. If your taxed income is below the threshold, then no card for you. The application process is largely automated, so I doubt there is any easy way around it unless you have a history with SEB kort or some personal relation with someone inside.

Since Entercard is jointly owned by Swedbank and Barcalys, you might be better of there since you already have a customer relation. But generally, getting any kind of credit is a hassle unless you have a "white" taxed income...

Low or no "white" income does not necessarily mean you are without funds!