I would say yes for some of them, and no for other.
Vegetarianism can be a moral norm, a cultural one. It can be enforced by law or by custom, even in societies where it is not necessary to solve cooperation problems.
Most cultures promote a vision of the world, of the society, of the relationship between man, society and world. This vision is an ideology, meaning a sum of ideas among which the necessity of promoting cooperation is not an imperative. Fears and prejudices are often their sources.
Matter is that the definition of what is moral can be very subjective.
One very common idea is that the body of women is erotic and is enticing men, by itself and that men have little self-control. One other idea is that women are inferior to men .
These ideas are not belonging to the morality, per se. But in some societies they were seen as such and were given legal weight.
The consequence is that women must hide their bodies. This idea gave birth to the idea that the women must hide their bodies. It became a rule as soon as in 1795-1750 B.C., in the code of Hammurabi.
From there, for the women, had to cover their hairs as a mark of submission, cf. Paul, 1 Corinthians.
The Muslim prophet did not invent anything, and his successors or some of them went to the extremes.