Zevachim 61a — the Talmud in English

This one

in which it was taught that sacrifices are disqualified

is Rabbi Ishmael’s:

for he derives the eating of flesh by a juxtaposition from the sprinkling of blood: just as the sprinkling of blood requires an altar, so too the flesh.

This one

in which it was taught that sacrifices are eaten

is the Rabbis’

for they do not derive the eating of flesh from the sprinkling of blood, and they hold that even in the case of a firstborn it is permitted to eat the flesh when the altar is defective.

And if you wish, say: both

the two baraitot deal

with most holy sacrifices

and deal even according to the Rabbis, who hold that only most holy sacrifices are disqualified from eating when the altar is defective, whereas lesser sanctity sacrifices are eaten when the altar is defective.

And what

was taught in the baraita

in two places,

“sacrifices are eaten,” means also

before the Levites erect the Tabernacle,

that is, when the Tabernacle is standing as prescribed,