Do you think favouritism should be banned in homes, as well as in schools and workplace?

It's impossible. Not to mention unnatural for human beings.

"My friend's father favors him over me."  Oh, the humility!  How do you plan on enforcing this law?

No. Some are still going to get born lucky into wealth, end up with the prettiest gf or the richest husband. Life never has been nor will it ever be fair. However, our religions were developed to foster fellowship and fairness as an ideal.

"Your friend's father favours him over me". Oh dear. Has it occurred to you that he does that because your friend's father naturally wants to encourage and show love to his son? You are not his son, so you are less important in this man's eyes. This is called filial love and you are not related. Get over  yourself.

To not show favourtism goes against the very structure of society, particularly where families are concerned and is unlikely to ever become law.

......and how do you think you could police a law like that?