Ibn Abbas (may Allah be pleased with them both) said that the Prophet (peace and blessings be upon him) said: "When a man says to another, 'O effeminate one (mukhannath)!', give him twenty lashes; and when he calls someone a Jew, give him twenty lashes as well."
Ibrahim al-Ashhali is alone in narrating it, and he is not strong; if it is authentic, it is to be understood as discretionary punishment (ta'zir).
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحدود / 17148
Sayyiduna Ali (may Allah be pleased with him) said that if a person calls another 'fasiq' (sinner) or 'khabith' (wicked), there is no fixed hadd (prescribed punishment) upon him; rather, the ruler should punish him by way of ta'zir (discretionary punishment) as he sees fit.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحدود / 17149
A shaykh from the people of Kufah said: I heard Sayyiduna Ali (may Allah be pleased with him) say: "You have asked me about a man who says to another man: 'O disbeliever! O sinner! O donkey!' There is no hadd (prescribed punishment) in it; there is only a punishment from the ruler. So do not go back to saying it."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحدود / 17150
Ubaydullah bin Abdullah said that Sayyiduna Umar (may Allah be pleased with him) used to flog those who made false accusations against the women of the people of the Millah. This is munqati' (disconnected). Even if it were established, it would be understood as ta'zir (discretionary punishment).
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحدود / 17152