Not the person you're replying to, but there is this persistent fallacy that left is inherently good and right is inherently evil, despite the fact that neither side of the political spectrum is inherently good or evil. Great injustices have been committed under both liberal and conservative governments throughout history.
Opposition parties are often anti-censorship, pro free speech etc. Once they come into power this all changes and they drift towards authoritarianism.
Western, left-leaning governments have invented the term "hate speech" to justify this behaviour, right-leaning governments would often use "family values".
Restricting hate speech protects the politically vulnerable, the minority, the oppressed. It's not a restriction on hate speech toward the government.
Restricting 'anti-family' speech protects the status quo, those in power, the political majority and oppresses the vulnerable minority. For example, look at the discrimination against LGTBQ people now.
