Do animals have different taste preferences within the same species?
Yes. Intra-species variation in food preferences has been observed in


Rabbits (Bilko et al. 1994)
Copepods (Rieber 1982; Berghe and Bergmans 1981)
C. elegans (Abada et al. 2009)
Earthworms (Bonkowski 2000)
Butterflies (Jermy et al. 1968)
Beetles (Sarker et al. 2013)


I am sure most pet owners will find the existence of this variation quite intuitive. No too cats have the same food preferences.

Why such variation exist?

I can think of several possible (non-exclusive and non-exhaustive) reasons for why such variation exist?


Individuals compete. If preferences vary, it allow specialisation (inspired from @John's comment)
Phenotypic variance (whether genetic, environmental or other) is not necessarily maintained by some kind of balancing selection. You may observe purely neutral variation in preferences.
Genetic variance can explain variance in food needs and therefore it is good that preference can be plastic
Same as above but for environmental reason. Say, an individual may have different need based on its environment.
One must learn to recognize good food. There might be a tradition among family of liking specific types of food.