Anyone know how to unlink Google apps on iOS?

I have multiple Google accounts. I used to be able to have one logged into Hangouts and another logged into Gmail, but now it's forcing me to use the same accounts on Gmail and Hangouts. If I log out of one, it forces me to log out of the other. I have looked through settings in both apps, but I don't see any obvious way of unlinking the two apps. Anyone know if there's a setting I'm missing to get this stupidity to stop?