Cheese can be a problem for gout; yoghurt not so much because it isn't as protein dense. The "biggies" for gout are seafood, red meat and turkey, red wine and beer (generally best to avoid alcohol) and legumes. I've also found that high sugar diets are bad including fresh fruit and juices.

I imagine that cheese and yogurt are significantly less than 100% bacteria. I couldn't find any easy numbers, but if I had to guess, it's less than 10% by mass for cheese.