Vegetarianism has been around for ages. Much of the vegetarian propaganda revolves around the aim of stopping cruelty to animals, it's one of the stated goals of the movement, if not the main one.
Some examples of such claims::
The average meat-eater consumes over 100 animals every year (or 270.0 pounds total). That means your decreasing the demand for slaughtered animals by 100 a year. Since about 7.3 million Americans are vegetarian, together we decrease the demand of animals slaughtered every year by 730 million (2 billion pounds of meat!)
A vegetarian saves more than 30 land animals each year.
By switching to a vegetarian diet, you can save more than 100 animals a year from this misery.
These quotes suggest, directly or indirectly, that people who do not eat meat have an impact on the number of slaughtered animals. Is there any evidence that the various herbivore movements have actually made any dent in the slaughter of animals in the food industry? Given their numbers and the time that they've been around, it would be reasonable to expect a visible effect by now.
Evidence is available of significant increase in meat-free sales. It's reasonable to expect a proportionate decrease in meat-based sales then, and a corresponding decrease in slaughter. Is there any evidence to the latter?