Written by Rabbis Eli Gersten, Yaakov Luban and Moshe Zywica of the Orthodox Union

Sefer Piskei Teshuvot (250:11) writes that one should only eat fleishig seudahs on Shabbat and Yom Tov (with perhaps the exception of Shavuot). He offers as a source the Leket Hayosher. However, in truth, the Leket Hayosher only writes that one should eat the traditional customary foods on Shabbat and that one should not change the traditions. 

However, it would seem that if one does not like meat, one is not required to eat meat on Shabbat. The Shabbat meal should be an oneg (delightful). One should eat what he enjoys. If he enjoys milchigs (dairy) and does not enjoy meat, then he may eat milchigs.

But as much as possible, one should try to keep the meal the same by serving the traditional foods. So, for example an Ashkenazi should still serve cholent and soup (just make them parve), still serve kugel and gefilte fish (if one likes fish), and other traditional foods. A Sefardi should do the same with the traditional Sefardic Shabbat foods. One should not serve macaroni and cheese or pizza as their Shabbat meal.