Can you give examples of rules / commandments in Islam that are largely rejected by modern rational society /people?

The most heinous teachings, such as the punishment of death for apostasy, come from the Hadith and not from the Qu'ran. Though, the vast majority of Muslims do follow the Hadith and consider it a moral guide.

Death punishment for apostasy:

Allah's Apostle said, "The blood of a Muslim who confesses that none has the right to be worshipped but Allah and that I am His Apostle, cannot be shed except in three cases: In Qisas for murder, a married person who commits illegal sexual intercourse and the one who reverts from Islam (apostate) and leaves the Muslims."

 Sahih al-Bukhari, 9:83:17.

Do note, however, that the Qu'ran makes it clear it is a sin to leave Islam, but as far as I know there is no mention of death.

Aisha's age upon consumation of marriage:

Narrated 'Aisha: that the Prophet married her when she was six years old and he consummated his marriage when she was nine years old, and then she remained with him for nine years (i.e., till his death).

This is from the Hadith (Sahih al-Bukhari, 7:62:64), and while the majority of the Muslim population accepts this as the truth, it's supposedly debated among scholars.

While not very explicit, there are many subtle hints that point at women being worth less than a man. It's not strange, however, seeing as the Qu'ran is a reflection of the society of that time, and it wasn't abnormal to consider women to be worth less.

Call in two male witnesses from among you, but if two men cannot be found, then one man and two women whom you judge fit to act as witnesses.

Qur'an 2:282

Men are the maintainers of women because Allah has made some of them to excel others and because they spend out of their property; the good women are therefore obedient, guarding the unseen as Allah has guarded; and (as to) those on whose part you fear desertion, admonish them, and leave them alone in the sleeping-places and beat them; then if they obey you, do not seek a way against them; surely Allah is High, Great.

Qur'an 4:34

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