I had little (and mostly bad) credit when I opened my first CU account. Wasn't a problem, at all.
It might, OTOH, be hard with the same kind of bad account history that will stop you from being able to open a regular bank account, but that's different from regular no credit or bad credit.
Most small and medium size banks don't pull your credit report. Its Chex Systems to see if you have any deposit accounts in bad standing. Some also pull fraud scores from experian or equifax as well to see if you information has been used in identity theft recently.