Most legal interpretations read that as a prohibition against government action. The Second Amendment has never been "incorporated" under the Fourteenth Amendment by the US Supreme Court. "Incorporation" in this case being an invented process suggesting that the Supreme Court shall determine which of our rights can be infringed by the states and which shall not.
To extend the protections of such prohibition to every person would suggest that it would be permissible to outlaw discrimination based upon all of the factors which today are still legal. Do you wish to give up the right to discriminate against Democrats? Even though Democrats have a right to freely choose their political party?
I am not opposed to a law which prohibits discrimination based upon bearing arms. I just think that politically, the chances of passing a law constraining only corporations would be so much greater.