There is a custom to refrain from bitter, sour or tart foods on Rosh Hashanah, to symbolize our hopes for a sweet, pleasant year. The Talmud declares that symbolic acts have significance. Therefore, one should not belittle the customs regarding the foods eaten on Rosh Hashanah as symbols of our prayers for the new year.
The Talmud declares that symbolic acts have significance.
There is a common practice to eat a pomegranate on Rosh Hashanah, as its abundant seeds symbolize our hopes that we will come before G‑d with abundant merits. Interestingly, the Ben Ish Chai (Rav Yosef Chaim of Baghdad, 1833 - 1909) writes that on Rosh Hashanah one should eat specifically a sweet pomegranate, and he emphasizes this point several times. Of course, the pomegranates we have today generally have a bitter, pungent taste. It appears that in Baghdad, where the Ben Ish Chai lived, they had sweet pomegranates. In any event, in light of the custom to refrain from bitter foods on Rosh Hashanah, it would seem proper to dip the pomegranate in sugar to at least diminish its pungency.

It is also interesting to note that the custom of the Ben Ish Chai on Rosh Hashanah was to dip an apple in sugar, and not in honey. Perhaps this custom was based on Kabbalistic teaching. Regardless, everyone should follow his family's custom in this regard. [Same goes for bread — my family keeps a bowl of sugar on the table until Shemini Atzeret, which the kids just love!]
The apples eaten on Rosh Hashanah thus symbolize not only sweetness, but also Paradise...
It should be noted that the symbolic significance of the apple on Rosh Hashanah extends beyond the simple fact that it is a sweet food. In fact, the Arizal (Rav Yitzchak Luria of Safed, 1534-1572) remarked that there is profound Kabbalistic significance underlying the eating of apples on the nights of Rosh Hashanah. The Zohar refers to Paradise as the "Chakal Tapuchin Kadishin/orchard of holy apples." The apples eaten on Rosh Hashanah thus symbolize not only sweetness, but also Paradise, which is certainly an auspicious sign with which to begin the New Year. Furthermore, the apple has a pleasing appearance, a pleasing fragrance and a pleasing taste. It is pleasing and enjoyable in every which way, symbolic of our hopes that the New Year will bring joy and success in all areas of life.

Furthermore, the Ben Ish Chai explained the significance of this custom on the basis of Kabbalistic teaching. During the period from Nissan until Tishrei, we are under the influence of the sefira ("emanation") of malchut, which is the lowest sefira and receives its strength from the higher sefirot. Once Tishrei sets in, we move into the sefira of tiferet, the higher sefira that gives to the lower sefirot. The sefira of tiferet is the sefira of Jacob, who represents Torah and who transmitted the power of Torah to subsequent generations. Tiferet is also associated with the attribute of "Emet" (truth), and on Rosh Hashanah we stand in judgment, which is based upon God's attribute of absolute truth. The apple, the Ben Ish Chai writes, is associated with the sefira of tiferet, and we therefore eat it on Rosh Hashanah, which marks the point of transition from the sefira of malchut to the sefira of tiferet.

Of course, the vast majority of us are not versed in Kabbala, and thus do not truly understand these concepts. Nevertheless, they demonstrate the depth and profundity of these customs that we observe on Rosh Hashanah. Besides the plays on words, such as "Yitamu Son'enu" ("Finish off those that hate us") for the "Tamar" (date), and "Yikartu Son'enu" ("Uproot those that hate us") for the "Karti" (leek), there are much deeper concepts underlying these customs, and we should therefore observe them in accordance with time-honored tradition.

If a person cannot eat one or several of the symbolic foods, either because he does not enjoy the taste or because of an allergy, then he should either look or point at the food while he recites the corresponding "Yehi Ratzon" prayer. He certainly is not required to partake of the food if he does not like it or is allergic to it, but he should nevertheless recite the prayer associated with the food, and this, too, will have a significant effect.

...it is proper to refrain from bitter and sour foods on Rosh Hashanah.

Thus, it is proper to refrain from bitter and sour foods on Rosh Hashanah. Pomegranates should preferably be dipped in some sugar before they are eaten on Rosh Hashanah, because they otherwise taste pungent. Some have the custom to dip the apple in sugar, instead of honey, and each person should follow his family's tradition. The customs regarding the special foods on Rosh Hashanah are based upon profound Kabbalistic concepts and thus should not be belittled or neglected.

[Rabbi Eli. J. Mansour is the Rabbi of Congregation Bet Yaakob in Brooklyn New York. The above is adapted from two articles on //dailyhalacha.com, one of Rabbi Mansour’s 7 (!) websites for Torah study.]