Here is a list of taboos:
- Religious beliefs. Not believing in God is OK, but it should be possible to freely criticize other people's beliefs.
- Sexual taboos. Bisexuality, swinging, S&M are all considered improper for no apparent reason. I won't dare even to hint child sexuality here.
- Nationalism. It is still considered perfectly normal to prefer people from your 'own' 'country' over people of another country. Tribalism is a very natural moral for obvious reasons.
- Political systems. Democracy is everything but perfect, but suggesting other forms of rule has not even been considered. A benevolent dictator will certainly be a lot better than a different charming elitist every 4 years.
- Drug use. Pot enjoys the popular vote, but XTC and other hard drugs are still very much not done. There are drugs which are inherently bad, but even most hard drugs aren't. Abuse is a symptom.
- Abortion (or further). Why are you not allowed to kill your own new born?
- Any criminal activity. These are just morals put to paper.
Any moral is a balance between human needs/wants and some theory about how society functions best. What really works best no one knows. It also depends on the goals. What constitutes a good society? The most productive? The one with the most happy residents? Evolution would say the one that survives. The moral fashions in that sense would equal genetic mutations in order to find the most optimal set of rules.
One thing is certain though. There are no such things as right or wrong moralities, there is only effective and ineffective moralities.