15th and 19th apply explicitly to citizens. US Citizenship is not a world-wide natural right. The natural right is to voting rights in your nation of citizenship to not be prejudiced by your protected class. Verifying votes are made by eligible voters in fact protect the 15 and 19th amendment from infringement -- imagine a scenario where a bunch of Idahoan men made a pact to come into California to [illegally] vote against state-level issues supported by female California voters.
How is that relevant? This thread is only about how the right to vote has to be considered when proposing ID requirements which would prevent someone from voting. Nothing about non-citizens, only what constitutes an acceptable burden for citizens.
The non-citizen consideration in inextricably linked to the citizen consideration. If you say something is specifically for citizens you're absolutely saying something about non-citizens.
The right for citizens to vote can only meaningfully be preserved by verifying votes are eligible, otherwise you could just bring in busloads of Mexicans or whatever and dilute the citizens votes to the point it was rendered a vote only in name. This is why it is harmful and deceptive to just frame this as a question about burden for citizens; if only citizens showed up to vote then obviously there needn't be any burden at all to verify citizenship. I reject your characterization as it being "nothing about non-citizens."
The 'burden' is there precisely to create an impassible, or at least fairly effective, impediment to NON-CITIZENS to stop them from voting. The question isn't what minimizes the burden of citizens (obviously not requiring any evidence would be least burdensome). It is what burden maximizes preservation of the right of the citizens to vote.
