You should drink milk that is only "COW" milk.Because it is considered under sattvik food.
According to "Bhagawad Gita (17.8/9)"-
'Foods dear to those in the mode of goodness(sattvik guna) increase the duration of life, purify one’s existence and give strength, health, happiness and satisfaction. Such foods are juicy, fatty, wholesome, and pleasing to the ...
First off, as Sheldon Pollock points out in his translation of Ayodhyākāṇḍa, the two verses you quote in your question have been removed from the Critical Edition of Vālmīki Rāmāyaṇa.
1. In order to establish a reasonable transition between sargas, the SR [Southern Recension] inserts
before this verse four lines (2091*), in which Rāma, ...
I acknowledge @sv.'s answer on this topic as authoritative.
Here is an additional reference for this issue, from the Manu Smriti:
After death the guilt of one who slays deer for gain is not as (great) as that of him who eats meat for no (sacred) purpose. [The Laws of Manu, 5:34]
The Mahābhārata says not only can deer be hunted but they can be consumed even without offering them to gods:
Desirous of benefiting all men, the high-souled Agastya, by the aid of his penances, dedicated, once for all, all wild animals of the deer species to the deities. Hence, there is no longer any necessity of sanctifying those animals for offering ...
The question is
how did this movement (Vegetarianism) spread to Hinduism?
Ramayana says (Kishkinda Kanda)
पंच पंच नखा भक्ष्या ब्रह्म क्षत्रेण राघव | शल्यकः श्वाविधो गोधा शशः
कूर्मः च पंचमः || १-१७-३९
"Raghava, five kinds of five-nailed animals,
viz., a kind of wild rodent, a kind of wild-boar, a kind of lizard, a
hare and fifthly the ...
What is influence of Jainism and Buddhism in introducing Vegetarianism to Hinduism?
Vegetarianism was already a part of Hinduism, and Jainism and Buddhism are religions founded based on Hinduism.
The fact is, according to Hinduism, meat can be eaten only if the animal is sacrificed in a Vedic yajna:
5.31 - ‘The eating of meat for sacrifices’—this is ...