Issues updating Xamarin: unable to resolve dependencies

I would extremelly recommend by 1 year of experience with Xamarin.Droid and Xamarin.iOS to only update Xamarin.Forms to latest version, and ignore Other Xam.Support Libraries unless is extremelly necessary to bug fix something that you need.

Reason #1: It is not fully tested by Microsoft.

Reason #2: You might need to spend hours configuring and fixing the references e version compatibility.

You can't update Xamarin.Forms and Xamarin.Android at the same time. As It has dependency issues with versions. So first, Select only Xamarin.Forms 2.3.0.107 and update. After that, Select rest of the Xamarin.Android.support lists and update.

According to me own experience, I would recommend to:

1. If your project is very old, try to migrate the list of your packages from packages.config to the .CSPROJ. Unlike packages.config, PackageReference lists only those NuGet packages you directly installed in the project. As a result, the NuGet Package Manager UI and the project file aren't cluttered with down-level dependencies. More info here
2. Clean the Nuget packages cache(s) : Tools -> NuGet Package Manager -> Package Manager Settings -> Clear All NuGet Cache(s)
3. Use the NuGet Console to get more details about you errors. Open the console (Tools -> NuGet Package Manager -> Package Manager Console), then type Update-Package
4. Always Clean and Rebuild after updating your packages

I'm quoting James Montemagno from the Xamarin Forums here.

Xamarin.Forms locks in a very specific version of the support libraries and google play services. You can't update them because Xamarin.Forms isn't compatible with them as it would need to be re-compiled.

Xamarin.Android.Support.v4 (= 23.0.1.3) Xamarin.Android.Support.Design (= 23.0.1.3) Xamarin.Android.Support.v7.AppCompat (= 23.0.1.3) Xamarin.Android.Support.v7.CardView (= 23.0.1.3) Xamarin.Android.Support.v7.MediaRouter (= 23.0.1.3)

See the = 23.0.1.3, which means it is only compatible with that version number. This is just how NuGet works. When Xamarin.Forms updates these packages will auto update.

Forms gets 'linked' to a specific version of the Android libraries so it can be guaranteed that it will work together as it should. At this point, Xamarin.Forms (stable) isn't updated yet to use the latest Android Support packages. So you probably want to go with a somewhat older version of Forms, or check if there is a Forms pre-release which already has a reference to the newer Android Support libraries.

Of course; using these is not recommended in a production environment.

They added it in the official FAQ