If you want to paint old varnished cabinets opaque, it is not necessary to completely strip them. However, you must first clean everything with TSP before applying a new finish. Then, you must sand the surface with 220-grit sandpaper to roughen the surface and maximize the adhesion of the new finish. 

You can use various furniture paints such as Fusion Mineral Paint, Chalk Paint, or Milk Paint without the need for a primer. If you choose an opaque lacquer, it is best to apply two coats of primer. Be sure to carefully read the manufacturer's instructions for the products used and take the necessary time to follow the guidelines.