Personally I'd find it kind of funny that this thing we use, on digital computers originally developed for the military, over the internet, originally developed for the military, using microchip technology originally developed for the military, and a hashing algo, originally developed for the military, that it would be a deal breaker if there were NSA involvement in the bitcoin protocol.
But I guess if you don't like it, you could just drive, over roads developed for a military (Google pershing map or Roman roads) and use the regular bank.
You are right, the vast majority of technology that is used today is somewhat based on something that was originally designed for the military. Even the technology that is used by social media has some roots from the military.
If you fear that Bitcoin was designed by the NSA/military and is therefore somehow insecure because of some kind of backdoor then you are wrong. Bitcoin is open source and many people have inspected the code and have put a lot of effort into finding weaknesses (including "backdoors") in Bitcoin