One who is incapable of eating a kezayit of matza (one third of a matza) should at least try to eat a portion of matza equivalent to a modern-day olive, because some poskim maintain that this is the true size of a kezayit. However, one may not recite the berakha of “al akhilat matza” over this amount of matza, because many poskim maintain that it is insufficient for fulfilling the mitzva to eat matza. Rather, he should fulfill the obligation to recite a berakha through the berakha of the Seder leader. If one cannot eat even the volume of a modern-day olive, it is still good to eat as much matza as he can, even a small amount.
Regarding one who knows that eating matza will cause him to become ill or intensify an existing illness but will certainly not threaten his life, the poskim disagree over whether he is obligated to eat matza: according to R. Shlomo of Vilna, such a person is exempt from eating matza on Pesaḥ (Binyan Shlomo §47), whereas according to Maharam Schick, a sick person is only exempt from eating matza where there is mortal danger (OḤ §260). The custom is to rule in accordance with the lenient opinion. (Regarding maror and the four cups of wine, which are rabbinic mitzvot, there is a consensus that one who will be consigned to bed if he eats them is exempt, as explained in section 7.)
According to this, most people who suffer from celiac disease must eat a kezayit of matza on the Seder night, because a kezayit of matza will not cause them to become sick. Even if it will cause one to suffer somewhat, this is not considered sickness. However, people who suffer from severe celiac disease, and who know that they are liable to have a strong reaction to matza, are exempt from the mitzva of eating matza. Nowadays one can find matzot made from oats, which is better for people with celiac disease.
. For the definition of one who is exempt due to illness, see R. Frank’s Mikra’ei Kodesh 2:32, which cites two opinions. Ḥazon Ovadia 1:33 and Tzitz Eliezer 14:27 are lenient. This is also what R. Harari writes in Mikra’ei Kodesh ch. 7 n. 110, in the name of Rav Mordechai Eliyahu.