I've been a credit union member for many years. My credit union survived the great financial crisis. There were CU failures, but the big problem was with what is called corporate credit unions. They offered services to customer based credit unions.
Before the GFC hit, I had a checking account and CD's with a big money center bank(BMCB) and played ping pong to get the best rates between my CU and the BMCB. At some point before the banking crisis took off, the BMCB started limiting electronic transfers leaving the bank. Of course there was no restrictions on electronic transfers going into the bank.
The final straw with the BMSB was they wouldn't let me terminate a CD prematurely online. I had to do it in person. The closest BMCB office was over a hundred miles away. I made the trip and closed out everything except my AA miles card..
Credit Unions are good places to bank. Have a Navy Federal account, credit card, etc - top notch.