How to Disable the Blue Check Marks on Android

Thankfully, due to a bunch of user backlash, WhatsApp has already introduced an option to disable the feature, but it's not available yet in the Google Play Store.
In order to have this option available, you will need to download the most recent Beta version of WhatsApp, which is currently only available for Android users. Head over to WhatsApp's official website, or just download the APK right here. The correct version you want is Version 2.11.444, and you will need Android 2.1 or above. Make sure "Unknown sources" is checked in your device's Security settings to install it.
Once installed, you can now go into the app and head to Settings -> Account -> Privacy and uncheck "Read receipts."

Now you can rest assured that messages sent to you can be read freely without WhatsApp notifying the other party. However, messages read and received inside Groups will still show read receipts, so there is no escaping that.