There are several plausible possibilities considering that the Season Two finale, The Wedding Squanchers, confirms that Bird Person knows Tammy to be a human. Any spoiler spaces below refer to this episode.
It is entirely possible that, as you say, Bird Person is "punking" Morty, but given that Bird Person respects Rick, he has treated Morty kindly during both of their encounters so far; I don't think that this is the case.
Tammy has never eaten in front of Bird Person, and if he knew she was human, he didn't think to ask her. Knowing Rick was a human, perhaps Bird Person never observed him eat any "human food" during their shared history.
Bird Person asked Tammy what Morty would eat. Tammy, who has shown a propensity for lying (per her actions at the party where she pretended to be drunk to seem "cool"), may be "punking" Morty by giving Bird Person incorrect suggestions.
Tammy has only eaten what Bird Person considers "random debris" in front of him, and Bird Person equates this to "random debris, which can be found in carpet", which he serves to Morty.
Tammy might not have exposed Bird Person to "human" food, and she is subsisting on whatever Bird Person is feeding her; possibly eating whatever he eats, or regurgitated Bird Person food as a bird feeds its young, or subsisting on something else entirely (considering Tammy's relationship to Bird Person, one can speculate...). Therefore, while Bird Person witnesses Tammy the human eating "whatever", he might not equate that to something that he can respectfully feed Morty the human.
6. Since it was revealed that Tammy was a deep cover agent working for the Galactic Federation, it is plausible that she, like her parents, was a synthetic humanoid, and therefore either didn't eat anything at all around Bird Person, or was unable to answer Bird Person's request for "human food" accurately. Even if she wasn't synthetic, she may have consumed whatever Bird Person ate and didn't complain in order to maintain a sense of stability for her cover (she didn't want to "rock the boat", as it were).
Notably, blatantly human food was not shown during The Wedding Squanchers wedding sequence. Therefore, it can be assumed that Bird Person (or the wedding planner; possibly Squanchy, since they were on Planet Squanch) determined certain non-Earth cuisine to be fine for human consumption.