The U.S. Constitution is the highest law in the land. If a law is held to contradict or violate the Constitution, then the law is void. This is not the case in many other constitutional democracies.
As for the question of whether an amendment could be enacted which permitted the persecution of a minority: yes, such an amendment could be enacted. Since amendments supersede contradictory law which was enacted before it, such an amendment would be valid and binding law.
The fact that an idea seems morally heinous or is stupid or impractical is not relevant to whether something can be part of The Constitution. The legality of slavery was recognized by The Constitution as it was originally enacted, with a provision that the importation of slaves would end twenty years after The Constitution went into effect.
Because the power of The Constitution is absolute, the framers intentionally made it difficult for it to be amended. While 27 amendments have been enacted, hundreds have been proposed and considered over the years, ranging from one abolishing child labor to one banning the burning of flags as an act of protest.
Making it difficult to pass an amendment is supposed to give people time to consider and debate proposed amendments sufficiently before they are enacted. This has not always worked in practice: Prohibition was permitted by one amendment, and then abolished by another.
This is one reason that a Constitutional Convention has never been convened to draft amendments. The framers of The Constitution were on unfamiliar ground when they framed it, and many of them thought it would be necessary after a time to tear it up and start fresh, guided my insights gained from the failings of their original effort.
This, obviously, did not happen. In modern times many people have expressed fear that a convention could result in a Constition which would be offensive to a large portion of the citizenry. For instance, some have argued that if a Convention was convened at the urging of people seeking to ban abortion, it might also enact provisions limiting freedom of religion to the “right” sorts of religions and freedom of speech to the “right” sort of speech.
“Due process” is an important concept which is difficult to define in exact terms. In fact, lawyers argue about whether something does or not amount to due process every day. Roughly, it means that a person is entitled to a minimal degree of fairness in the way the government conducts itself with respect to you, particularly in a court of law.
For instance, American courts must sometimes rule whether or not a person was granted minimal due process by a foreign government, in order to see if the U.S. should recognize that government’s decision. Another nation might give a defendant far fewer privileges while on trial. If the defendant is entitled to face and question his accusers, and has adequate access to information about the laws of that country and his rights under them, and can present evidence in his own defense, though, a court in the U.S. will likely find that the person was afforded due process and will let a decision stand.
Another example: if an American couple obtained an uncontested divorce in The Soviet Union, the U.S. would consider the people to
be married. This is because uncontested divorces were granted there merely by signing in a registry administered by civil servants. There was no hearing, and no judge. This meant that there was no legally trained authority who could advise the parties of the consequences of their actions and verify that they understood these consequences and were proceeding willingly. In other words, there was no minimum due process.
“Equal protection” is also difficult to define, and many, many laws have been struck down on the grounds that they did not grant it. Roughly, “Equal protection” requires that laws be applied so that there is not an arbitrary or unfair distinction drawn between one group or class of persons and another. One of the most important meanings of this in the years immediately after the 14th Amendment was ratified was that it assured that full rights of citizenship were granted (at least in theory) to former slaves: they had a right to vote, to serve on juries, to seek public office, etc.
Often the issues which come up in a discussion of equal protection are more arcane. Iowa had (and perhaps still has) a law saying that a person must be a resident of the state for a prescribed period of time before he or she can file for divorce there. It was argued before The Supreme Court that this denied equal protection of the laws to people who had only recently moved into the state. The Court ruled that this was not a violation of equal protection, after concluding it served a legitimate state interest–namely, that the state did not wish to become a destination for people seeking “quickie” divorces.