Sorry about getting the state wrong, I was thinking it was California due to a previous, unrelated post. I am only familiar with the details of California's ecosystem and cannot intelligently comment on New Jersey or most other areas.
In California, there are a fair number of mountain lions, but the bear issue is a human-caused one. California Grizzlies were native to California and were a top predator. Once hunted to extinction, they were then artificially replaced with the Black Bear, which does not hunt large game like deer. They are much smaller bears and have a completely different role in the ecosystem. So the fact that there are more is unsurprising, since they are effectively an invasive species. The mountain lions are currently taking on the role of hunting from both wolves and grizzlies, so it would make sense if there are more needed for deer control.
With rattlesnakes, I was referring to California alone, where the California Ground Squirrel is extremely overpopulated. In California, the rattlesnakes are one of the primary predators of ground squirrel young (they eat a lot of babies, relatively fewer adults). Though the total population of rattlesnakes is fine, often where human populations and wildlife meet, the rattlesnakes are locally underpopulated and there is an explosion of ground squirrels. While this is not a threat for rattlesnake extinction, there then exist extremely high densities of squirrels which are more likely to carry nasty diseases right next to where people live.
Regarding livestock, I feel there is a difference between actively protecting a herd and using guard dogs and shepherds and just simply slaughtering any predators (and deer/bison/etc. that carry diseases and compete for resources) that cross over onto your property. Many grazing animals today are not well herded due to myriad factors, and overall I feel that is irresponsible. One outlandish solution is getting rid of all the non-dairy cattle and their feed crops in places where bison were native, and instead let the bison deal with the predators on their own and we simply sustainably hunt the bison.