Incorrect. Unlike the First Amendment, which starts with Congress shall make no law, ... the Second Amendment has no qualifiers. The right of the people to keep and bear arms shall not be infringed. This should legally strike down as moot the New York law, any church, school, bar, or courtroom prohibition, any individual store, residence, etc. provision. However, a business could exercise the right to refuse service (but not the right to carry).
You correctly read the Constitution when you read it as written and originally understood and intended. If a clause is clear, you take it as is. If a clause is unclear or ambiguous , then you look to the the original understanding of the clause and the intent of the ratifiers. The intent of the RATIFIERS, who turn a proposal into law and who turned the Constitution into the Supreme Law of the Land and created the Untied States of America, is dispositive in correctly interpreting and applying the Constitution.
A look at the the background of the first 10 amendments will tell you that Madison wrote them as an answer to the antifederalists who did not want a federal government because they were afraid it would become what it now has become 250 years later. As a way of getting the antifederalists to join in ratifying the Constitution, Madison and the Founders promised they would include the first ten amendments to at least clarify to the nay-sayers some of the most important right of the people and the states those that already belonged to them.
The LAST thing the antifederalists, critical to the ratification of the Constitution, would agree to would be ADDING MORE power to the federal government.
The only powers delegated to the feds were those enumerated in the body of the Constitution. Anything limiting the states were also in the body on the Constitution. States were limited by only a few things like prohibitions from coining money and making treaties. These things are clarified in the 9A and the 10A. (The first 10 amendments were ratified 3.5 years after the Constitution was ratified.)