It's not like mammalian herbivores are a recent invention. If a constant amount of mammalian herbivores in the world would cause a constant acceleration of greenhouse effect then the greenhouse effect would have increased exponentially for millions of years already. That has not been the case.

If you increase the number of mammalian herbivores in the world then the greenhouse effect will increase for about a decade because of increasing levels of methane. After a decade, the methane level (and therefore the greenhouse effect) will have found a new (higher) equilibrium and no longer increase.