With a certain portion of people, the protein in oats is close enough to the other glutenin proteins to also cause a reaction, so its generally recommended to cut it out for that first year to make sure its not also a problem. The thing is, even a small reaction will keep any healing from happening, so the symptoms won’t go away. And its also harder in that first year to figure out exactly what you are reacting to.
I’d stay away from it for the first while (6 months minimum, but a year would be better) just so you have a really good idea afterwards if it causes you problems or not. If after a year you have no trouble with oats, it opens up a bunch of food options for you. That healing time really matters to let you know later what is actually reacting to you, its shocking how much you condition to over time.