“It is a matter of allegiance”
What lies behind this simple statement settling the issue for certain minds is the entire madness of the style of Constitutional construction known as “original intent.” You divine that they were interested in preventing all but those with birth allegiance from being president, and therefore conclude no one with possible dual loyalties can possibly be president.
It matters not what they intended, but what they say. What they intended can help elucidate what they said, but it cannot add to it. The Constitution does not say “No person except those born without possible loyalties to other nations shall be eligible to be President.” That’s what you think it says, or want it to say, based on your pinpointing the allegiance motivation. However, just because they were motivated by concerns over allegiance does not mean native borns aren’t also natural borns. Especially since the 14th amendment came so long after the Founder generation.
Common sense was much more common in the days of our founders.