Do you have anything against vegetarian food? We could go to a different restaurant.

have 在这里是助动词，构成疑问句的基本结构，表示"拥有"或"持有"。 against 是介词，本义是"反对、对抗"，在这里表示"对...有意见/不喜欢"。 have something against 是一个固定搭配，意思是"对...有意见/不喜欢"。