This happens on some iOS devices
To play the game you need to sign in with an existing account from either Google or Pokemon Online. The second one is not accepting new signups so people are forced to use their Google accounts.
The thing is, when registering, you see this:
Pokemon Go has full access to your Google account
Meaning that Pokémon go is able to read all your email and send emails as you, full control on your Google Drive, full control on your search history, full access to Google Photo and so on.
They aren't obviously looking to steal all your data, but this is too careless.