Apart from the obvious ones like slavery, violence, systematic persecutions of minorities — which, btw, are still practiced today around the world, so let’s not pretend we have the moral high ground here — there is one thing that today is a taboo, both for the act itself and the meaning behind it.
If you were an unmarried woman, you had to kiss your brother or your father on the lips every morning.
Now, Romans had some weird attitudes towards kisses in general: they used to kiss on the lips even friends they met on the streets as a sign of greetings and respect, until the Emperor (I think it was Tiberius) had to officially prohibit it because it got out of hand and people were complaining. But kisses as signs of affection between lovers were something they seemed to be uncomfortable with and couples who kissed in public were frowned upon. French kisses were a brothel exclusive foreplay.
Ius osculi (“the kiss right”) was another thing entirely and it was mandatory: in the morning women had to kiss the man of the house (so their husband, father or brother) to prove they hadn’t secretly been drinking during the night.
That’s weird enough, but what’s even worse is the reason for this practice: wine was known to provoke abortions, so it was a strictly prohibited substance for women. The woman who was found out drinking — and so forsaking her duty as baby-maker — could be put to death.