We were there in July of 2020 and saw several people tent camping. There was also a host at this particular site that had been in there for the last 5 years (very nice people). So, in my opinion, it is a safe place to tent camp.
It has been more than a year since I stayed here. Hopefully, someone with more recent experience will respond but safety is relative to the precautions you take these days. The advice I give myself and others is if something does'nt feel right then move on to a different area. I found that there was a lot of people using the dispersed camping area that while not as responsible and considerate of the area and others they did not seem a threat to my safety. The wildlife as well are not a threat unless given a reason to invade your space. here is a link to the National Park Service about Bears and people interaction: https://www.nps.gov/grte/planyourvisit/bearsafety.htm
Hope you enjoy your trip.
Yes. Just take the normal precautions when camping in areas with bears. The majority of bears are further north in the park. Moose, elk and bison are more prominent in lower Grand Teton.