I’ve worked in a factory making sausages/hotdogs/etc. I’ve also worked on the kill floor and pretty much everywhere- I and comfortable eating meats.
Hotdogs are fine to eat. No eyeballs or hooves
When you have a steak, it’s essentially a sliced roast. Sometimes the ends are not big enough to be sold as a steak, or the middle is TOO big, or there is a bruise on part of it that needs to be cut out, or abscess from an injection, etc so the steak can’t be sold as a steak (wrong shape/size once the bad part is cut off)- the misshapen good part of the meat that is left goes into the hotdog. Cuts that, for some reason, can’t be sold as a roast or steak are used. IIRC, organ meat cannot be used, either. “Generic” hamburger is also made this way (ie those not labeled ground chuck or whatever).
Now, I would look into nitrites/nitrates. For that reason, I limit my families consumption of processed meats to 1-2x a month. This would be deli meats, salami, balognise hot dog, sausages, ham, bacon. Notice that the “healthy” ones say “no nitrites added.” The process of curing the meat still gives cause for the development of some, but generally MORE are added to this to help with shelf life- even if none are added, they are still present to a degree.
Pink slime aka finely texured beef (or chicken) doesn’t bother me any. I make it myself when I crock-pot a roast, and pick out all the non-meat pieces.

I just can’t do it as thoroughly as I could if I ground it up, then used a machine to separate the fat and meat. You grind it, heat it up (to melt the fat), and use a machine to separate the fat and meat. You then use ammonium (was most common when I did this- other things can be used) to make sure any potential bacteria in it is killed, and ammonium is considered GRAS.