Should I have natural yoghurt with a fat meal or a carb meal?

If you have a fat meal you can have any kind of natural yoghurt – even full fat Greek yoghurt if you like it (or crème fraiche or fromage frais). With a carb meal you would need to have (very) low fat natural yoghurt /crème fraiche/fromage frais. This is why you can have skimmed milk with cereal, as the milk is so low fat it is OK to have with the carb. Not mixing fats and carbs takes a bit of eff...