Since it is get from the exploitation of innocents mammals, consuming milk and dairy causes bad karma?
My answer is based on the info found on this page.
From Mahabharata Anusasana Parva
Bhishma said: No sacrifice can be performed without the aid of curds and ghee (clarified butter). The very character of sacrifice which sacrifices have, depends upon ghee. Hence ghee (or, the cow from which it is produced) is regarded as the very root of sacrifice.
Hence, it is evident that one of the purposes for which cows exist is to produce milk from which ghee can be made.Hence it is evident enough that the act of obtaining milk from cows can't create bad karma.Instead it is good karma since you are aiding in agnihotra(fire sacrifice) which is essential for sustaining the Demi Gods who in turn sustains life.
More from the link.
Cows have been said to be the limbs of sacrifice. They represent sacrifice itself. Without them, there can be no sacrifice. With their milk and the Havi produced therefrom, they uphold all creatures by diverse acts. Cows are guileless in their behaviour. From them flow sacrifices and Havya and Kavya, and milk and curds and ghee. hence cows are sacred.
Let's now see what saints have to say on consuming or using cow milk.From the same link :
Cows are sacred. They are embodiments of merit. They are high and most efficacious cleansers of all. .....For the next three days one should drink the hot milk of the cow. Having thus drunk for three days hot milk, one should next drink hot ghee for three days. Having in this way drunk hot ghee for three days, one should subsist for the next three days on air only.
So when a self realised Rishi like Vyasa is recommending drinking milk the act of obtaining milk from cows can't result in bad karma.
By bathing in water mixed with cow-dung, people shall become sanctified.... Cows are the best Havi for the deities. The Mantras called Swaha and Vashat are forever established in cows. Sacrifices are established in the cows. Cows constitute the fruit of sacrifices.Cows are the future and the past, and Sacrifices rest on them. Morning and evening cows yield unto the Rishis, Havi for use in Homa......Cows are the mothers of the universe.*
So, again, it is quite evident from the above quote that being the mother of the entire universe a cow's duty is to feed everyone with her milk and not alone her own calves.Such is the greatness of cows.
I'm concluding my answer with another Bhisma's quote:
Cows are the mothers of the universe The human infant is fed breast milk by its human mother for under three years. After weaning, the cow acts as the surrogate mother providing milk for the rest of the human life-through childhood, adult age and old age. Cow is verily the mother of the world.
So, obtaining milk from cow is in no way a bad karma provided you are not forcing her or inflicting pain on her in any form.Also ,her calves should not be deprived.