It wouldn't be simpler for the people being discriminated against. Working, shopping, banking, trying to find a place to live. Wondering if the people coming to pull you from your wrecked car are going to approve of your color, religion, sexual orientation, etc., as well as the hospital they take you to.
Not very simple for the folks who find it distasteful as well. There is an attraction to libertarianism (allow people to do anything so long as they are not using force against one another or engaging in fraud), but it has it's own ugly edge to it as well. I think it may be worse.