Steps to reproduce:

1. Create new project and build as Universal 10 target
2. Open built solution and at the end of MainPage.xml.cs constructor add:
var simpleWebView = new WebView();
simpleWebView.Source = new Uri("https://google.com");
var someDialog = new ContentDialog();
someDialog.Content = simpleWebView;
someDialog.ShowAsync();
3. In Package.appxmanifest enable Internet Capability
4. Run solution
5. In search bar type anything. Notice that you can type until splash screen shows up

Not reproducible: 5.3.3p2
Reproduced with: 5.3.6p6, 5.4.1p2, 5.5.0b5

Why won't fix: Unity cannot properly detect when different XAML elements get focused because not all of them tell us they're focused, so we cannot reliably stop processing input. A workaround in this case is to call UnitySetInput(false) when you show WebView and call UnitySetInput(true) when you want Unity to start processing input again.