Most of the times yes. I only buy products that may contain traces of egg, milk or whatever when I do not have any other choice avalaible and I'm startving. Otherwise I prefer not to buy them just to be on the safe side

mostly yes

Milk, I'm not too worried about, although I try to be careful due to dairy intolerance and possible skin allergies (it's not certain but dairy may have been giving me eczema).

Egg, I have to avoid though because idk I'd rather not pass out or have my throat close up I guess?

Basically, I try to avoid them based on allergies, rather than my ethical reasons for not eating any animal products whatsoever. I've noticed that the "may contain traces" term is quite outdated now and the term "made in an environment that handles" is often used instead. Which makes much more sense really.