The mishna says that the only type of eating that qualifies him as a ben sorer u'moreh would be an optional eating, to the exclusion of a seudas mitzvah and to the exclusion of eating things that are assur. The gemara 70b clearly says that the source for eating of issur not qualifying is the pasuk which says איננו שומע בקולנו which we darshen to mean - בקולינו ולא בקולו של מקום. Rashi explains that the only type of rebellion that he can become a ben sorer u'moreh on, is when he rebels ONLY against his parents, to the exclusion of one who doesn't even listen to the voice of Hashem.
There are 2 difficulties with this gemara: 1. The source of the gemara works well to explain eating of issur, but what is the source for eating of mitzvah not qualifying him as a ben sorer u'moreh? 2. The gemara includes in eating of issur even the eating on a ta'anis tzibur which is only d'rabonon. How does the torah itself recognize an eating that is only forbidden m'drabonon as not being included in the optional eating to qualify him as a ben sorer u'moreh, since m'doraysa it is an optional eating?
Regarding the second question, the maharatz chiyus writes that according to the Rambam (hil. mamrim 1:2) that there is a mitzvah to listen to the chachamim and one who violates a d'rabonon essentially violates an issur Torah, it is understandable that the Torah can recognize even an issur d'rabonon to qualify as "issur" and not render him a ben sorer u'moreh. It is far more difficult to work this out with the Ramban in sefer hamitzvos who argues on the Rambam and holds that violating d'rabonons is not a d'oraysa violation. According to the Ramban how does the Torah recognize issurei d'rabonon to qualify as issur that wouldn't render him a ben sorer u'moreh? Perhaps the drasha doesn't come to exclude the eating of issur, rather the pasuk comes to exclude any type of rebellion that is provoked or motivated by something other than rebelling against his parents. The eating of an isssur d'rabonon is also not provoked by rebelling against his parents alone, but is also provoked by a will to rebel against the Rabbonon. This is very meduyak in the Rambam (pirush hamishna) - לפי שנאמר "איננו שומע בקולנו" ועד שלא יהיה באותו המעשה שלו אלא המרות אביו ואמרו בלבד ולא המרות התורה. The pasuk isn't just excluding rebelling against the torah, but is excluding any eating that is not JUST a rebellion against his parents such as issurei d'rabonon. This approach would work even for the Ramban who disagrees with the Rambam.
Regarding the first question, the source for mitzvah eating not rendering him a ben sorer u'moreh, the gemara says that we limit the din of ben sorer u'moreh to cases where he is likely to be drawn after it. Any eating of a mitzvah will not be likely to draw him after it to continue stealing to indulge. The rationale seems to be that since the eating for mitzvah purpose is constructive, not for indulgence alone, it will not draw him to become a glutton. However, the Rambam (hilchos mamrim 7:2) groups the mitzvah eating together with the aveirah eating and writes - נאמר "איננו שומע בקלנו" שאינו עובר באכילה זו אלא על קולם, יצא זה שעבר בה על דברי תורה או שאכלה בדבר מצוה
The Radvaz in his commentary points out that the Rambam doesn't take the simple reading fo the gemara that we are only concerned of eating that will instigate more stealing. Rather, the Rambam understands that the very same pasuk which excludes an aveira also excludes a mitzvah. As we were medayek from the Rambam on the mishnah, the pasuk teaches that he only becomes a ben sorer u'moreh when the impetus to eat is for the sake of rebellion against his parents, to the exclusion of one who does an aveira who is also motivated to violate the will of the Torah AND excludes one who eats for a mitzvah where the eating is provoked and motivated by the intention of doing a mitzvah (this would include even a mitzvah d'rabonon).