I have a Moto E gen1 and android 5.1 installed on it. After factory reset , google play services crashes every time, whenever i try to login to my account. Apart from this login problem everything is working smoothly.
Maybe just try to go in developers mode Google service, google+, app store etc stopped working
I tried all the recommendation to clear cache, etc etc and after the factory reset still getting the error. What finally worked for me is going to Developers mode (easy to do, search how to for you phone in google).
I bet some developer tested something and push his code to PROD without testing real user mode. Once I did, the error magically disappeared.