So it’s made of shit, right? And shit is an animal product. But barring a night of drinking or a particularly aggressive burrito, shitting does not harm the shitter; it’s beneficial and required. Also the animals in question can and do consent, does that make it vegan?
“They only produce milk after having been pregnant” is just a dumbed down way of saying “pregnancy is what releases the hormones that stimulate lactation”. The point still stands that mammals do not lactate at all times.
https://en.wikipedia.org/wiki/Galactorrhea