Maciej we need a little more information.
Is this an iDEAL payment or a direct debit. In both cases they may not refuse bunq. If bunq is not listed in their iDEAL list on the page, than that is a breach of terms of "Currency iDEAL B.V.", the company that offers iDEAL, their rules state a company must update the list at least once a month.
For direct debits, bunq processes and accepts them the same way as any other European bank. In this case the SEPA regulations also prescribe parties to update accordingly.
If they use iDIN for verification and identity purposes, again a service from "Currency iDEAL BV", they are even required to update bi-weekly.