Even though the character says she is vegan, she isn't. As pointed out a duck dinner plus she mentions she drinks milk.
Also when she leaves high school and goes to NY she tries cooking duck herself to impress a guy in season 4. Also in Season 4 she says she is vegetarian at thanksgiving.
Also she didn't mind receiving a pig that was being raised to be slaughtered. Her only concern was that it wasn't bling.
The actress Lea Michele is just following a vegan diet
. So she isn't vegan but a strict vegetarian following a plant based diet.
This is a common misconception with celebs.