Do all banks pull credit reports to open a checking/savings account? Is there a list of which ones do and which ones don't?

I am assuming if they don't use Telecheck or ChexSystems they pull credit reports. Is that correct?

It really depends on the specific bank ..they are all different. Some of them (especially if you go to a local one where you can present an ID will not run a credit report.) But most times if a bank does not use chexsystems or telecheck, yes they will run a credit report ( some run them as identity verification only and others run them as a source of credit worthiness)