If I make a skillet full of bacon, how long can I leave the grease sitting out before it is unsafe/rancid? Is the answer different for ground beef grease?
Fat doesn't spoil like other foods. No bacteria can live in fat. Going rancid is a chemical reaction in which the fat molecules break down. So "leaving out" is not a problem.
The major factors in going rancid are light and air. The more light hits your fat, the sooner it goes rancid. Also, rancidity occurs when the fat is oxidized, meaning that if you prevent contact with air, your fat will last longer.
Both factors are minimized by transferring the fat to a tightly closed opaque container. With liquid oils, you use a dark colored bottle. As bottles are impractical for solid fat, just strain your grease into a jar, close it, and put it in a cupboard. The shelf life should be many months, probably more than a year.
Also, don't worry that you can get something nasty when the grease goes bad unnoticed. Rancid fat isn't a big safety risk, and ingesting it in small amounts is not problematic. If it stinks, throw it out. Before that, there is no problem eating it.
The above assumes pure, well-strained fat. Pieces of fried meat left over in the fat are a safety risk, even tiny ones.
Grease makes an anaerobic environment that is, that it lacks oxygen and while that may prevent many types of bacteria from growing in it (Staph.,E. coli,etc.), Clostridia species (including the kind that causes botulism) are obligate anaerobes they need to have an oxygen poor environment in which to live.
Now, will all that scalding grease allow bacteria to live in it? As more is collected, it mixes and rapidly cools when it melts the existing grease.
Although our grandmothers may have collected grease and kept reusing it, people used to die a lot younger "back in the day" as well, just saying.
When it comes to food handling, better safe than sorry. Once it cools, store it in the refrigerator where it will keep for up to a month without fear of bacterial overgrowth.