Grammatically the 2nd Amendment is a mess. For a bunch of learned scholars there seems to be a lot confusion over how to use a comma or put clauses together to create a coherent sentence.
Just the same that clause "the right of the people to keep and bear arms, shall not be infringed" seems pretty cut and dry. What it doesn't do is address anything regarding how such a right would be regulated. Conservatives seem to argue that this gives a blank check as far as what kind of weapons one may bear, but this is ludicrous on the surface; obviously you can't keep nuclear weapons, dirty bombs, working tanks, etc.
So yeah, based on the wording of the 2nd Amendment, the people definitely have a right to bear arms, and the government has the right to regulate that right, as with every other right in the Bill of Rights. For example, free speech - it's completely protected, except in some situations, not being allowed to yell "Fire!" in a crowded theater being the classic example.
Such restrictions are in place to protect the populace, as are regulations on weapon ownership. Obviously by the letter of the Constitution such regulations are not unconstitutional. What's more, such regulations have broad bipartisan appeal. That's why any time regulations are introduced, or people even start talking about regulation, the NRA has to amplify it to "They're gonna take our guns away!" so gullible Republicans will oppose it.