Shulchan Aruch writes that a ger may not curse, humiliate or hit his non-Jewish parents so they should not say that he is on a lower spiritual level since his conversion. The Rambam adds that he must show his parents a limited degree of honor and respect, while the Tur writes that he does not honor them at all. Reb Elyashiv shlita explains that there is no disagreement, while the specific halachos of kibud av v'eim do not apply, basic appreciation for their having raised him is imperative. There are specific halachos regarding the degree of contact a ger should maintain with his former family which are outside the scope of this answer.
The Gemara is clear that one need not listen to his parents if they tell him to do something that is against Halacha such as eating non-Kosher food, even inadvertently. However in such a situation it is necessary to analyze the exact specific Kashrus problems that may arise and determine if there is truly any issur to eat the food. In many cases the food may be permitted to eat even if it was prepared in a manner inconsistent with Halacha. It is necessary to determine each incident on a case by case basis with great sensitivity for the parent's feelings, as they apparently mean well and must be treated with respect.