Is cheese a common noun

Yes, the noun cheese is a common noun, a Word for any cheese of any kind.

A proper noun is the name of a specific person, place, thing, or a title; for example:

• Wisconson, 'America's Dairyland' or 'The Cheese State'
• Cheese Road, Petersburg, TN or Cheese Run Road, Indiana, PA
• The Cheese House, Plain City, OH
• "The Long Quiche Goodbye: A Cheese Shop Mystery" by Avery Aames