Today's daf (Chulin 7) tells the famous story of the donkey of R' Pinchas ben Yair that would not eat dmai. The gemara asks: We learned in the Mishna (Dmai 1:3) that animal food is exempt from dmai -- why would the donkey not eat? The gemara answers that the food was purchased fo human consumption and was therefore obligated to be treated as dmai. Only food originally set aside for use as animal food is exempt.
The Yerushalmi gives a different answer (Dmai 1:3; 4a in the Vilna edition). According to the Yerushalmi, R' Pinchas ben Yair said, "What do you want from me -- my donkey is a frummie."
Moral of the story: one can be a frummie and still be a donkey.