When an app on iPhone tries to log in through Google, must it be Safari? Can it be Google Chrome?
Unfortunately, no.

It is not possible to set a different default web browser on iOS. though in some applications you can specify this, that is few and far between. 

So generally speaking if you need to log in to a service and it needs to open a web browser you can have it open in any browser as long as the browser is Safari.

It would be nice if that were different but the powers that be at Apple, so far, have said no to that feature.