If a piece of a biblically forbidden food (such as a piece of pork), falls into a bowl of meat. We all know the rule, it's batul bshishim. How about a piece of food which is only rabbinically prohibited (a food that contains דברים מעמידים such as cheese). If the cheese would fall into a bowl of other cheeses, would the same laws of bitul apply regarding the shishim part. Or would we be even more meikel, because the food itself is only rabbinic?
Assuming I understand your question correctly, batel b'shishim applies to both rabbinically and torah prohibited foods. It's basically the ratio at which chazal felt a tiny quantity of food became relevant.
However keep in mind it only applies to food when you can't separate the two foods. If a piece of non-kosher cheese fell into a bowl full of pieces of cheese, I see no reason why you wouldn't just pick it out.