It seems to me that there are already plenty of laws that breach the 1st amendment if you interpret speech as absolutely any speech (e.g. death threats, libel, ...). And it is constitutional because the current interpretation of speech is narrower than "everything".
Doesn't that mean that, if there were the will to do it, free speech could be reinterpreted (by the supreme court?) to not include hate speech, thus not requiring to change the 1st amendment?
If there really was the will to do it, it would be by passing a constitutional amendment. If you aren't familiar, there is a process by which the constitution can be modified, and this can be done to completely rewrite or contradict the current text. But it's a very difficult hurdle: https://en.wikipedia.org/wiki/List_of_amendments_to_the_Unit...