Certain fields are used to set up the standard data model and are used Marketing Cloud internally. It's dependant on the Marketing Cloud Connector and these default settings cannot be modified.
Contact ID etc are all part of the default set of fields will always be part of the Contact object when you want to set up the Synchronised Data Extension.
If you are going to be utilizing Marketing Cloud Connect, these settings are just something you'll need to live with. Though as there are many other limitations to the Connector, it's not very unusual that major businesses develop their own, custom 'Connector' between CRM and Marketing Cloud to have full control over what is synchronised.
This means that the regular features like Journey Builder canvas actions, creation of Individual Email Results and all like that need to be custom developed as well, so think twice before going that route.