UPDATE: The Pokemon Company International and Niantic Labs have released a statement about this issue, which can be found here. The original story runs below.
The iOS version of Pokemon GO has a potentially troublesome privacy feature. If players use their Google account to log into Pokemon GO, the game automatically grants Pokemon GO "full account access" to your Google device. This technically means that Pokemon GO can view and modify nearly all your information in your Google account, including emails, contacts, and documents.
The flaw only occurs on iOS devices, so Android users don't need to worry about Pokemon GO having access to your emails and contact information. You can revoke Pokemon GO's access to your Google account by clicking on this page.
There are a few different ways to protect your privacy while playing Pokemon GO on an Apple device. You can create a throwaway Google account used specifically for the game, or skip Google all together and create a Pokemon Trainers Club account to play the game. It should be noted that due to the immense amount of traffic caused by Pokemon GO, some players have complained of having issues logging into Pokemon GO using their Trainers Club log in.
If you don't want Pokemon GO to collect this information on your phone, you can contact Pokemon GO's privacy email (email@example.com) to opt out, although it could impact how the game works on your phone.