Unfortunately, Xcode 8 doesn't allow you to easily switch to manual code signing for new projects (which default to automatic code signing, and that requires an Apple ID for a valid developer account). If you want to switch the project to allow manual code signing (so you can use the code signing identity provided by your client), you must make some manual changes to your .cxodeproj file.
First, make sure you have closed the Xcode project. Then, find your xcode project (.xcodeproj) in Finder and right click on the icon, then select "Show Package Contents". Inside the Finder window, find the "project.pbxproj" file. Right click on that file and open the file in your text editor of choice (you can open this in Xcode). Find all occurences where you find the text "ProvisioningStyle = Automatic;" and replace it with "ProvisioningStyle = Manual;". Save the pbxproj file and then re-open the .xcodeproj in Xcode. You should now see options for specifying the code signing identity in your project settings.
You can find some more details about this, including ways to script this in this answer.