What is the etiquette for picking up dog poo in fields or off the beaten track?

I know this is a slightly crude and disgusting topic but it's really been bugging me.

I take my dog on a variety of walks including footpaths on a roads where I always pick my dog's waste up (in public), but when I go via the back of my house through the fields I usually let my dog go and leave it, as long as it's not along the main public footpath.

Additionally the field is already full of cow pats and sheep droppings... However I was challenged by a lady the other day who stated cow/sheep poo is very different to dog waste so I should pick it up, even if it's off the supposed beaten track. She stated that it would affect the milk, even though I responded with the cows in the back of the fields behind me are all heifers (male)...She then said it would affect the taste of the meat when sold, which I thought was total rubbish.


Thanks
David