The most common way that flu vaccines are made is using an egg-based manufacturing process that has been used for more than 70 years. Egg-based vaccine manufacturing is used to make both inactivated (killed) vaccine (usually called the “flu shot”) and live attenuated (weakened virus) vaccine (usually called the “nasal spray flu vaccine”).
The other two methods are not vegan either. The other one uses mammal cells and recombinant vaccines use animal testing in most cases.
Bit unfortunate that they add a banner with political propaganda on top of government pages these days. Including health-related topics. Not saying this specific article has to be wrong, seems it’s from a few years ago, but I double-check everything that comes from the US government these days. Could be true, could be some narrative or wild lies. Especially if related to vaccines.