I support it 100%. That has been the law-of-the-land since the earliest days of our nation. Except for one glaring and outrageous period of time when Native Americans, even those born here, did not receive automatic citizenship and had to be 'naturalized', but ONLY if the men agreed to serve in the military and the women married someone who was already a citizen. As recent as 1957, there were still laws on the books in some states that prevented Native Americans from voting in local elections, irrespective of their citizenship status.
But now that you've broached the subject, how about people NOT born in the US but who were granted citizenship due to a parent being a citizen?