The term buttoned-up is not referring to wines. It is referring to the white wine gals. The columnist that wrote that article was comparing the white wine gals to the red wine sisters.
In this situation, buttoned-up is used to describe the white wine gals as being more conservative than the red wine sisters.
Examples of conservative:
Your Grandmother is more conservative than your parents. Your parents are probably more conservative than you are.
Sally's Mother will not let her wear a dress that shows her knees. Her Mother is too conservative.