"Safe" is always relative. Nothing in this life is completely safe.
So, you have this nice looking bit of land that happens to be radioactive.
Given a choice between eating the food from there and other food, you would choose other food.
However, given a choice between that food and NO food, you would choose radioactive food.
So, you eat what is available, you might get cancer many years from now but at least you aren't starving today.
In the same manner, people are still evacuated from Bikini and Chernobyl because they can. If they had too they could move back and live there. They would have a slightly increased risk of cancer, but life is full or risks anyway. Smoking is still more risky.
The limit comes when people die faster than childbirth replaces them. But this limit is very high. A mere nuclear war won't come close. (In long term effects, that is. People caught a bit too close to the initial blast would have problems)