Parashara smriti is said to be a valid text for people of Kali yuga.
Does Parashara smriti allow the eating of non-vegetarian food?
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Parashara Smriti (PS) does not have many verses dedicated to the topic. Meat eating, in general, is allowed when it is part of a sacrifice done in the honour of gods and/or manes. Otherwise it is not much recommended but still not entirely prohibited (this can be proved using a Manu Smriti verse). So, we can assume, Parashara does not have to say anything entirely different in this regard and so he does not say much.
Beef and some other meat are of course considered as forbidden food in the text.
If a Brahman has partaken of any impure food, or has swallowed virile seed, or beef, or a Chandala's food, he should perform a Krichchhra-chandrayana.
After knowingly eating the meat of a frog, or of a mouse, a Brahman will become pure by taking unripe barley as food.
And, we have the following verses too, which clearly show that abstaining from meat is what is recommended, even for the Sudras.
If a Shoodra be addicted to flesh meat and spirituous drinks, and constantly engaged in low occupations — he, like a member of the Swapaka caste, should be shunned by a Brahman from afar.
A Brahman should never shun such Shoodras as are employed in the service of regenerate men, abstinent of spirit and flesh meat, and duly employed in their own occupation.
Other than these verses, there is nothing much in the text on the topic.
(All verses are from chapter 11 of PS).