Aside from the constitution, why are citizens allowed to purchase semi automatic rifles?

Because there is no “aside from the Constitution”. You have appreciated the American system opposite to how things work here.

You ask why we’re ‘allowed’ to do something? It doesn’t work that way. We Americans can say, do, own, buy, sell, possess whatever we want. We’re not ‘allowed’ anything. We need no ‘permission’. Read the whole Constitution, including the Bill of Rights and you’ll find nothing among the powers given to government, by the people, saying we must first seek to be allowed to do something.

This is the main difference of the American way where we are free citizens not government subjects. America has the ethos that anything not explicitly banned is allowed. Not that anything not explicitly allowed is banned.

To stop, ban, or restrict this freedom, a law, eventually found to be ‘constitutional’ if someone thinks it isn’t and takes it to court in our judicial system, must be passed in the legislative political process. Not the other way around.