DNA would fall under “accidents”, and Catholics don’t believe that the accidents usually change. DNA isn’t part of the “is” of something, it’s a trait that’s subordinate to the “is”. The substance is the “is”, and hence “transubstantiation”.
Here’s a little illustration that might help you out, or might confuse you more, but it’s worth a shot It’s not a perfect example, and it has some definate flaws, but it might get you going in the right direction.
Imagine your mother. Imagine all her features, her personality, her personhood. Now, we would all agree that you are indeed imagining your mother, in that the woman in your head is most definately your mother and not anything else, but the “mother in your head” is made up of electrical signals in your brain, whereas your mother is usually made up of atoms and walks and talks on her own. Both people, the person in your memory, and the person walking around, are your mother, but they have distinctly different “accidents”, or ways in which they present themselves; one is memory made up of electro-chemical impulses, and the other is a carbon-based lifeform with a human soul. You know that you are remembering your mother, however, because the “is” is the same, the underlying fact of the person is the same. You aren’t imagining anyone else, and you certainly aren’t thinking of electro-chemical impulses.
Remember, this isn’t an exact depiction of what’s happening with the Eucharist, but it helps to illustrate that the non-essential features of something aren’t the basis by which we identify it. A more direct correlation might be hearing a person’s voice over a speaker, and hearing it directly. The accidents are different, as one is in the form of an electrical impulse through a machine, and the other is in the form of the vibrations of their throat, but both are absolutely the voice of the person. The substance is the same.
In the Eucharist, the substance of the person that is Jesus, the Son of God, comes to us through the accidents of bread and wine. Your Protestant friends are mistaking the accidents for the substance, which is completely absurd when put in the context of everyday things like memories and recorded speech.
That being said, there have been times in history when the accidents did indeed change, and they are recorded and preserved. You can begin reading about them here. In particular the Miracle of Lanciano is well studied and documented, and continues to be evaluated by scientists. By the way, if you’re curious, Jesus apparently had AB blood (the rarest blood type), as the Shroud of Turin, the Sudarium of Oveido (the actual cloth that covered the face of the dead Jesus), and the Eucharist of Lanciano all have AB blood, and they were around long before blood type was known about.