Translation:The religious women do not eat milk and meat.
I don't know if it's actually wrong in french to say this sentence with "and" (is it?) but I think both is more or less correct and depends just on your usage and/or intention. The idea behind the "and" instead of "or" is that you negate the unity of the things you're listing afterwards, whereas "or" would negate them individually. F.i. you would more likely say "i don't eat meat and (drink) milk" if it is somewhere written or said you should not eat both of them (or: neither of them), but maybe you would say "i don't eat meat or (drink) milk" when the milk is an addendum - because you're allergic to it or whatever.
I believe the sentence to mean that milk and meat cannit be consumed at the same time based on the religious practice. So using the "and" helps to attach the two nouns with the singke action. "They may eat meat or drink milk, but they cannot consume meat AND milk at the same meal."