Under what circumstances should government be able to limit natural rights?

When they conflict with the public interest.

Explanation:

(APEX)

It depends on where you are a citizen, like the US or Ireland. I'll assume you mean the US. In any case that the government needs to limit one of the Americans Citizens Natural Rights, it's most likely that they're trying to protect the citizens. Although it's probably very unlikely that this will ever happen. If it ever does, they'll basically be breaking the Constitution and the Bill of Rights. Which is technically not allowed.