You're forgetting that people can (and do) already take guns everywhere else outside of national parks, and there are still plenty of wildlife out there.

I can hike locally where bear, cougar, moose, deer, coyotes, and other wildlife are plentiful and easily found, despite the fact that people can (and do) take guns there.

If I thought that guns in a national park would mean any significant impact on tourists or wildlife, I'd be against it, too. But my experiences outside of the parks leads me to believe that it would work out just fine in a park.

The places where you see a serious impact on wildlife are in close proximity to small towns. The locals go out and shoot things for fun. Any time I'm within five miles or so of a small town, wildlife becomes scarce to none, and spent casings and trash become the norm. But in any area that's even remotely similar to a national park, that's just not the case.