So if someone from Guam or Puerto Rico wanted to run for President and actually won, would you accept them as President?
They are territories and not states.
Yes, they are territories, they are citizens of the US, they can vote in our elections, and do, because they are citizens. Where did you ever get the idea that people born in territories were not citizens. Every state in the Union after the 13 original colonies, were territories at one time, all of the residents could vote because all of the residents were citizens, and natural born citizens at that. If a Puerto Rican ran for President they would be eligible.
If you are going to ban people born in territories you had better include McCain because he was born in the territory of Panama(it was at the time).