If customer objects to certain processing, like e.g. marketing or exporting data to third countries, is controller or processor allowed to deny all services to the customer? If yes, then actually there is no real 'right to object'?
The right to object to marketing is an absolute right so no controller cannot deny you that right. Referring to the right to object to other types of processing, any request must be assessed by the controller and if there is no legal ground for the processing activity; for example there is no legitimate interest then the processing activity must cease. However keep in mind that certain services cannot be offered to individuals without processing their data so in this case the services will have to cease being offered.