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.