You can absolutely sync your Apple contacts and calendar with your Android.

The free method takes a little workaround which I will describe first. There is a paid method which will cost you a few bucks, but I feel, far less hassles.

First the free method...

Now...if you want to do all that, it works. That is the way I originally started syncing my iCloud contacts and Calendar with Google.

Then I discovered two paid apps that will do it automatically for you without having to lift a finger...

SmoothSync for Cloud Calendar

SmoothSync For Cloud Contacts

My advice is spend the $6-7 for both these apps. They work well for me and the updating is more instantaneous than it was with the manual methods I described above.

Let us know what you ended up doing and how it is working for you.

PS: If you use Smoothsync, both applications require to download their free Workaround tool. You will see it listed in the program description.