From yesterday I started getting this issue in iOS emulator:
When I hit cmd+D in iOS emulator to bring up development menu, App becomes unresponsive for ~30 sec. Then w
In case you are having trouble with emulators, you can at first use a physical iOS device to circumvent the issue. The react native menu does not freeze there (tested).
Periodical freezing of the screen can happen if you are using apps that use accessibility features, like e.g. BetterTouchTool or SizeUp with Xcode versions 7.0 and 7.1 and the issue should be resolved in Xcode 7.2 beta as discussed here.
If that doesn't help, try disabling Slow Animations
as described in the accepted answer.