I just recognized that react-native 0.24.1 on Android 4.x devices fails to connect to HTTPS servers which allow only TLS 1.2, e.g. following Mozilla's recommended "modern compatibility" configuration [1].
According to the Android documentation TLS 1.2 is also supported on Android API level 16+ (Android 4.1+), but enabled by default only for API level 20+ (Android 5.0+) [2]
If using Android's native SSLSocketFactory implementation, it is quite simple to enable the TLS 1.2 support [3]. I am not sure though, if and how this is also possible for react-native applications. I also do not know why the Android developers did not enable it by default, so there might be any downsides on doing so. Therefore a config option to turn the support on/off would probably be a good idea.
I would like to create a pull request for this but before digging into the react-native code I wanted to create this issue in case someone else is able to push me in the right direction (or even say it's impossible).