Nothing is 100% without risk, but each layer of safeguard reduces it. The standard shouldn't be zero risk, but rather weighing the risk of one (in)action vs another.
To draw an analogy to the obvious vaccine-related situation on everyone's minds, no one who knows what they're talking about would say that mRNA covid vaccines are 100% safe. But they are far, far safer than not having a vaccine, so it makes sense to accept that risk. I'm not saying the same is necessarily true of any given 'contagious' animal vaccine, but it could be.
To draw an analogy to the obvious vaccine-related situation on everyone's minds, no one who knows what they're talking about would say that mRNA covid vaccines are 100% safe. But they are far, far safer than not having a vaccine, so it makes sense to accept that risk. I'm not saying the same is necessarily true of any given 'contagious' animal vaccine, but it could be.