THis has been discussed elsewhere. Elves did eat meat else they would not have hunted I am sure - and you may recall that Elrond provided fur lined clothes for the fellowship, which would have been an odd thing to do if they were vegetarian. There is no indication that Legolas refused the ham cooked by Merry and Pippin at Isengard and since it is made clear he doesn't smoke, I am sure vegetarianism would have been mentioned!
The fact is, meat unless dried like billtong, is not practical for travellers to carry with them and it takes time from the journey if you have to hunt or fish for it. I thought it was ludicrous that in FOTR that the few cooking scenes were of sausages at weathertop/caradhras ... botulism would have saved the Nazgul and Saruman a lot of work
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Meat was a luxury until recently - originally in steak and oyster pie the oysters were there to bulk out the precious steak and ,in France , servants had it written into their contracts that they could not be given salmon more than twice a week. What we regard as luxury items (at least pre-fish farming), were staples pre pollution. Meat production requires a stable, agricultural community and since Rohan and the Shire are in this category it is no surprise that meat features more in their diets. For Hunter-Gatherers the food supply would be more erratic. But in general none of the communities had the luxury to choose their diets. As long as it was fit for consumption it probably got consumed.
I do wonder actually about Elvish food production especially in Lorien . Mirkwood traded with the lake men and I suppose Rivendell must have had some agrigulture though I doubt the deep valley provided much suitable land - but I imagine that Rivendell was a faily small community compared to the other Elvish settlements.