According to this interpretation, arguments supporting capital punishment is hate speech and should be banned.
Remember that whenever you create a tool to silence people, you are building a weapon that can be used against yourself. As recent elections have shown, sane politicians aren't always in power. The only long term solution is to build a system that works even when your enemies are in charge.
Even in Europe, which has much stricter bans on hate speech and xenophobia than the US does, and where capital punishment is banned, claiming capital punishment should be unbanned is legal.