there is no species barrier

There are a few things to unpack here.

First, most of the bacteria, et al. that we have to worry about right now from meat production and consumption are already well-adapted to human hosts. The solution, in most cases, is to adequately cook the meat, and to practice very basic food safety at home. Most food-borne illnesses are the result of inadequate cooking time and temperature. Other toxins--like botulism--are actually a biproduct of bacteria that colonize meat during putrefaction; you can kill the bacteria that produce the botulism toxin, but once it's present, there's not a lot you can do. (This is why you refrigerate meat. Clostridium botulinum reproduction is primarily room temperature, and anaerobic, so it's mostly a problem with canned goods that weren't sterilized properly during canning.)

The same solution to bacterial contamination in meat now would be the most effective solution for any lab-grown meat: cook your food correctly.

you’ll create a swamp of human meat factory farms that use huge amounts of antiviral, antifungal and antibiotic agents

I think that it's unlikely that, aside from cleaning agents, that you would need antibacterial/antifungal/virucidal agents in producing lab-grown meat of any kind. Many of the most effective cleaning agents work because there's no way to evolve protections against them. 70% isopropyl alcohol for instance; any resistance that bacteria evolved would also severely inhibit their ability to have any other functions. You can use radiation, or heat + steam (or even dry heat) to sterilize all of your equipment prior to introducing cells, and you have more control over the nutrient bath that it grows in. Depending on the nutrient bath, you can sterilize that by filtration; .22μm filtration is the standard for sterilizing IV and IM compounded medications. (.22μm is smaller than all bacteria, and many viruses. Molecules will still pass through that filter pore size though. You can also get filters down to .15μm if you need to remove more viruses.) Cows, chickens, etc. use so many antibacterials because they aren't able to put them in ideal conditions and maintain the desired production levels.

I think that the lack of a species barrier is a far, far smaller risk than you might believe it to be.

BUT.

I think that there is one enormous risk: prions. Misfolded proteins are exceptionally hard to detect, and anything that denatures them will denature other proteins as well. The risk is likely very, very low, given how uncommon prion diseases are, but it's definitely a risk when you can grow a culture indefinitely.