Can DNA from the food you eat “sneak into your DNA”? No.
Does GMO DNA have some secret power allowing it to insert into your DNA or the DNA of your gut microbes? No. And No.
Image: dGMP (single deoxyguanosine monophosphate nucleotide)
Humans and every other animal on the planet have been eating DNA for as long as they’ve existed. Self-replicating living organisms by definition contain DNA. Whenever you eat food, whether it be plants, animals, fungi, yeast, you are ingesting DNA. Fragments of ingested DNA can be briefly found in the intestinal tract and blood, regardless of the food source. There are no known instances of DNA, or genes, being transferred from food, “transgenic” or otherwise, to either community of bacteria in your guy or to the cells which comprise your tissues or organs.
After eating any food, the ingested DNA is rapidly degraded by various digestive enzymes, first to small DNA fragments of various sizes and subsequently down to nitrogenous-sugar building blocks of DNA. Tiny DNA-fragments, individual DNA nucleotides with a single base (A, T, C or G), can be taken up by the body or intestinal bacteria, but these fragments are not functional genes any more than a few letters can be said to form a meaningful sentence.
Individual nucleotides are treated metabolically similar to the way individual amino acids (the single building blocks of every protein on earth), are during food ingestion. Amino acids and single nucleotides are the building blocks of life; without which you wouldn’t exist. There is no difference between the small amount of extra DNA inserted in the plant by genetic engineering and the large amount of existing plant DNA which it is added to in this respect. If it weren’t identical, it would be completely useless.
So, what is the take home?
Humans have been ingesting DNA even since they’ve been eating food (all living things contain DNA). Regardless of where the DNA you just ingested comes from, you are not going to obtain new genes or get ‘foreign DNA’ inserted into either you or any of the other 100 trillion bacterial cells living in and on every part of your body. No, GMO DNA can not “sneak into your genome”, nor will the DNA of the bacon you ate for breakfast or the DNA from the orange juice your drank.