Unfortunately, there are some people who belittle the "Simanim" the special foods that we eat on the two nights of Rosh Hashanah to symbolize our hopes and prayers for the coming year, such as the apples, dates and leeks. They mistakenly feel that eating these foods is of no significance, and they therefore do not bother to observe this time-honored tradition.
It must be emphasized that this custom is rooted in the Talmud, which states explicitly, "Simana Milta" the use of "signs" to express our hopes and wishes is effective and meaningful. Indeed, eating foods that symbolize our hopes for the new year can have a significant impact and effect upon the coming year. The Gemara draws proof from the ancient custom to inaugurate new kings by a fountain of water, as a symbol of the nations hopes for an everlasting dynasty that continuously "flows" like a fountain. This demonstrates that symbols are meaningful and effective in fulfilling our wishes. This can be understood either in terms of a spiritual effect caused in the heavens through eating the Simanim, and is mentioned in several books, or on a purely psychological level, that eating sweet foods, for example, impacts upon our psyche and draws us toward joyful, purposeful pursuits such as Torah and Misvot. Regardless, one must not belittle this tradition which has its origins in the Talmud, is codified in the Shulhan Aruch, and has been practiced for centuries. In fact, the Arizal (Rav Yishak Luria of Safed, 1534-1572) remarked that there is profound Kabbalistic significance underlying the eating of apples on the nights of Rosh Hashanah. Clearly, eating these foods is far more significant and important than we might think at first.
If a person cannot eat one or several of the Simanim, 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 Rason" 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.
Summary: One must not belittle the importance of the Simanim the special foods eaten on the nights of Rosh Hashanah as symbols of our hopes for a successful, sweet year. These customs are rooted in the Talmud and are, indeed, beneficial in our efforts to fulfill our wishes for the coming year.