You know one situation that I find extremely hypocritical? Mustangs in the Western U.S. Are eating endangered plants and walking over delicate rangeland, therefore trampling the native spores, etc. That's not good. However, native animals eat those same plants and walk in those same areas, but only Mustangs are targeted as invasive. Why? Because they're non-native. They're an easy target.
However, one must take into account that the Mustang population once numbered in the millions and today they only exist in the low thousands. The same goes for bison and numerous native species. Obviously, since Mustangs once lived in populations much larger than they do now and were not causing this kind of trouble back then (otherwise the land would completely destroyed) it becomes obvious that something has changed since white Americans arrived, and that that something has upset the natural order, displacing Mustangs and causing them to live in and eat things they didn't use to.
Fortunately, the answer is clear as to what has changed: cattle. Domestic cattle and sheep number around 4 million on public lands. They outnumber Mustangs 50 to 1 in most states, and 200 to 1 in others. That's 3 million more than there ever were of Mustangs on those same lands, and 160% more than the modern Mustang population. The huge cattle and sheep populations have pushed out native wildlife and Mustangs, displacing wildlife and causing them to live in and eat plants that are unatural for them to eat. Although cattle are rotated seasonaly, there are still millions on the land at any given time. Even when a space of land is evacuated, it is typically so run-down that wildlife do not move back into it. Thus, cattle move back and keep the land as their own. Even though it's clear that cattle greatly outnumber Mustangs and are also forcing Mustangs and other wildlife into unatural and often inhospitable areas, anti-Mustang groups continue to argue that Mustangs, not cattle, are the true invasive animal. They say that because Mustangs are non-native, that they are automatically invasive. However, they completely ignore an enormous factor in the equation: cattle and sheep, the other non-native species. It's not logical to ignore the more abundant, newer, non-native animal and choose to accuse the rarer non-native animal that has lived in North America for hundreds of years longer, and also lives in populations much, much smaller than it used to, back when the ecology of the land was relatively harmonious. Since Mustang populations are lower than they ever have been, pro-Mustang groups say that it's not logical to pin all the blame on the horses.