These are known issues in React Native 0.40 (reported in React Native github project as issue #11736) that occur for others (myself as well) on a fresh project.

As of 17 minutes ago, there are a number of pull requests which reduce some of the issues.

One commenter on the issue reports that "Those are warning and you can mostly ignore those warning. You project should run fine with those warning." I've confirmed this, but hopefully we'll get these warnings cleaned up soon.

Why

The OS Deployment target is way too low for many of these dependencies. Some are set to iphone 4! I created a bug in React Native with this same solution

Solution

1. Copy function min_OSTarget_post_install into your Podfile
2. Call the function within post_install
3. pod install
4. See hundreds of Xcode warnings dissapear

Code

def min_OSTarget_post_install(installer)
  installer.pods_project.targets.each do |target|
    target.build_configurations.each do |config|
      if Gem::Version.new('8.0') > Gem::Version.new(config.build_settings['IPHONEOS_DEPLOYMENT_TARGET'])
        config.build_settings['IPHONEOS_DEPLOYMENT_TARGET'] = '9.0'
      end
    end
  end
end

post_install do |installer|
  ...
  min_OSTarget_post_install(installer) // ADD THIS  LINE
end