>I assume for people who eat meat there's the additional concern of antibiotics resistance due to the antibiotics given to livestock.
The concern isn't eating meat from an animal treated with antibiotics infecting you with resistant bacteria.
The concern is treating animals with antibiotics puts evolutionary pressure towards breeding resistant bacteria that spill into the ecosystem and eventually get back to us. But not through meat consumption, it effects everyone regardless of diet.
Specifically: animal waste is sometimes used as fertilizer, and sometimes that waste isn't treated properly to eliminate pathogens. Sometimes you're eating antibiotic-resistant-waste-laden plants, and sometimes those plants are fed to animals that humans then eat. Same for aquatic plants/animals downstream of animal waste. Even drinking water can be contaminated.
Antibiotic resistant bacteria isn't the only harmful downstream effect of factory farms of course. Regular-old harmful bacteria are in the runoff, as well as super-high levels of nutrients that harm waterways, plants and animals. Algal blooms, oxygen dead zones, contaminated water table, etc.
All because we really like cheap pork, beef and chicken.
I'm not saying eating a bit of cow poop on your lettuce never gets anyone sick, but that's not the mechanism of concern.
One: poop is mostly bacteria, by mass. It isn't infected with ... it is. Some can be "pathogens" but that's what the last stage of digestion is, fermentation with mostly a wide array of bacteria.
The concern is these gut bacteria developing antibiotic resistance and bacterial infections in the animal developing resistance. Then infections are spread between animals and across species and the waste is reintroduced into the environment. Resistant bacteria in the environment share. Horizontal gene transfer between species of bacteria can lead to these resistance genes being popular and everywhere. It's not cow poop infecting you, its the genetics getting spread into the environment and eventually ending up in a human pathogen.
>animal waste is sometimes used as fertilizer
More or less all industrial farmed animal waste ends up as fertilizer. Also a major component of the kinds of soil we grow crops in is bacteria, much of which has been through the digestive system of an animal. Again I don't know what people think soil is. If you want "clean"(?) never been poop growth medium for your plants you have to go completely artificial. And manure isn't sterilized before it goes into fields, it's alive.
The concern isn't eating meat from an animal treated with antibiotics infecting you with resistant bacteria.
The concern is treating animals with antibiotics puts evolutionary pressure towards breeding resistant bacteria that spill into the ecosystem and eventually get back to us. But not through meat consumption, it effects everyone regardless of diet.