What could be done to US states that openly allow non-citizens to vote?
I notice that the other "answers" don't actually address this, which is presumably the question at hand. Not which law is supreme or whether it runs afoul of federal law. As I understand it, the question is what can be done if California or another state ignores binding law in terms of electing federal representation. The presumption is that the law is constitutional and supreme.
TL;DR: The answer to the original question, as stated, is probably nothing. Nothing can be done "to" states that openly allow non-citizens to vote. However, that does not mean that nothing can be done. The states require the active assistance of the federal government in having their voting results count. The federal government could refuse to accept the tainted election results.
As a general rule, there is no "punishment" for states that do not follow federal law. At best, withholding of funds related to that federal law. Instead, there are mechanisms to enforce federal law. For example, Dwight Eisenhower sent military troops to Little Rock, Arkansas to enforce Brown v. Board of Education, which was a legal decision mandating desegregation nationally (although it was determined based on conditions in Topeka, Kansas).
In this particular case, the most likely mechanism would be to disallow election results that were not in compliance with federal law. So if the state allows non-citizens to vote, the federal government might throw out some or all of the state's votes as invalid. Again, this is not a punishment, but an attempt to work around the recalcitrant state. However, this would have the effect of disregarding the state's wishes in terms of representation.
The most modest result is that nothing would actually change. Some votes would be thrown out as tainted, but the final result would stay the same. More impactfully, the election result might change, so the federal government recognizes a different winner than the state does. At the extreme end, Congress might refuse to certify an electoral college result, so only the other state votes would count.
Refusing to certify the electoral college vote has happened in the past. In the presidential election of 1876, an Electoral Commission was appointed which chose between electoral college results offered by some disputed states. This had the effect of swinging the election from Samuel Tilden to Rutherford B. Hayes.
In Congress, this could result in the state's choices for Representative and/or Senator not being seated.
It's not clear to what extent this "punishes" the state. If the state did not allow non-citizens to vote, presumably it would have had different election results. Perhaps the state would prefer no representation to that different representation. Perhaps it would make no difference. For example, Congress currently has Republican majorities in both chambers and Donald Trump won. If the 2016 results had been refused, Congress would still have Republican majorities in both chambers and Trump would have won.
It's also worth noting that these results might not happen. If Congress is controlled by people who sympathize with the state, then Congress might accept the election results even with non-citizen votes. So if the Democrats take the House and Senate in 2018, they will determine what results are accepted in 2020.
If the Supreme Court were to get involved, it might create a constitutional crisis. In theory, accepting election returns is a prerogative of the legislative branch. But they have passed laws purportedly binding them. If they do not follow those laws, can the Supreme Court overrule Congress? We don't know, as it has never been tried.