One of the major benefits I think would occur would be that it would help root out and stop it. When the vast majority of society sees discrimination as wrong, those that do it will get branded with the stigma of their actions. Currently there is no actual cost to the bigotry behind discrimination for most people. By allowing it to come out in the open, society can be deal with. When people have to hide it, then it simmers and results in explosive and violent venting that can result in dead people.
It is also an infringement of rights. It infringes people's rights to choose who to associate with, trade with, and deal with. Whenever a law infringes a right it create hostility and more often than not, it is not the law that is the target of the hostility, but those the law was trying to protect. Things such as reverse discrimination, racial or gender quotas, and so on are all sources that bred resentment in people, highlighting people's differences and creating disharmony between them.
By making it a socially driven thing rather then a legally driven one, it also more likely to gain acceptance. People are more likely to change their minds and accept things if it is their peers who are driving it. If the people around them shame them for their actions, then they are more likely to change their ways than is the Government demands it. The Government telling people what to do breeds resentment in them, and they are likely to dig in deeper, rather then accepting the rebuke and teaching that their neighbour would give them.
Which one has more impact, your friends and family shaming you for drinking and driving, or the Government telling you that you aren't allowed to?
We see this in a lot of things. Drinking and Driving was illegal a long time without the rates doing much. It wasn't until it started to become socially unacceptable to drive and drink that we saw the numbers reduce.
Likewise smoking is not illegal, but as it becomes more and more socially unacceptable to smoke, we see the numbers dropping substantially.
Consider the figures here. Tobacco smoking is legal but becoming increasingly socially unacceptable and the rates have dropped from 40% in the 60's to 15% today. MJ smoking is illegal but becoming more socially acceptable and the smoking rates are estimated to be as high as 45%.
In the same way, by making discrimination socially unacceptable, and defusing the resentment that people feel about being told by the Government what they can do, the discrimination will decrease and people will be more enlightened about things rather then clinging to their hate and bigotry.