If no vinegar will the cheese cake be ruined
I've no idea what recipe you're looking at. I have many recipes for cheesecakes of varying types and not a one of them calls for vinegar in the recipe.
After looking at that recipe, I would think you could just omit the vinegar with no deleterious effect.
I used to make cheesecakes for several restaurants in Portland and none of them contained vinegar. Can you post a link to the recipe?
Agree with ChefJune. The only thing I can think of is that the recipe writer wants the cheesecake to be more tart. I would recommend instead finding a different recipe.
Originally, red velvet cakes used both vinegar and buttermilk to cause the cocoa to turn a reddish color. Then the recipe changed and red food coloring was added. You don't need it in the cheesecake.