Apparently Princess Di started her AIDS advocacy work in the late 80s. As far as I understand, we knew HIV was sexually transmitted in the early 80s.
So there is a bit of a difference - Princess Di knew she was safe shaking the hand of someone with AIDS, whereas anyone hanging out with lepers around 0 AD, probably wouldn't have known whether they were safe.
I'm not saying that to diminish Princess Di's advocacy, but there is a difference in the expected risk. It may be fair to argue that Jesus would have plot armour thanks to being a demi-god (or the chosen of one), so he wouldn't really be assuming risk either.