It is not a limit. There is no "only" or similar limitation in that clause. A justification is not a limit. It is not a reasonable position to add words that are not there. The only way to take that position is to ignore the rest of words actually written down: "the people" "shall not be infringed".
A justification can quite easily imply a limitation: to the extent the justification does not apply, then there is an argument that the right does not apply, either.
If it had read "protection from wild animals being necessary to a free state, the right of the people ...", then it would be pretty clear that where no such protection was needed, the right would not attach. Thus, there would be a good argument that the right only attached in places where wild animals might be found loose, and therefore did not apply in, for example, cities.