The default conservative interpretation of the Bill of Rights is that they are natural rights and that the purpose of those amendments are to specifically prohibit the government from usurping them. In that light, anyone — resident or not — should be allowed to be bear arms in the United States.
The problem isn’t that an illegal immigrant should or shouldn’t be allowed to bear arms, it’s that there’s a known illegal immigrant who isn’t being transported to the nearest border in the first place.
Legal aliens are allowed to buy, own and carry guns so I don't think the issue is citizenship. Criminal behavior comes with sanctions.