The Constitution requires that the Federal government MUST ensure that every State has a republican form of government. One of the requirement of a republican form of government is that ONLY citizens may vote. Citizens have civic responsibilities that non-citizens do not. They have requirements of loyalty that non-citizens do not. They can be compelled to public service (based on the results of votes) that non-citizens cannot. It is an outrageous violation of the rights of citizens to allow non-citizens to vote.
This is simply inaccurate. Wisconsin allowed non-citizen immigrants (primarily Scandinavians and Poles) to vote in local elections over a hundred years ago. There is nothing prohibiting this in the U.S. Constitution. In fact, the practice has long-standing historical precendent. That's not to say it is required or even a good idea -- just that there's nothing illegal about it.
When it comes to federal elections though ....