The entire premise of this thread is that there ought to be a legal right, not that one currently exists (or else this thread would be redundant).
How about we divide the law into categories: the public sphere and the private sphere (this is not talking about public and private law, but something different). Matters in the public sphere involve people's interactions as members of society. Matters in the private sphere involve personal relationships. So the diagram would look something like this:
| Public sphere | Private sphere |
- Employment
- Housing
- Education
- Government services
- Shopping
- Transportation systems
- Voting and political participation
|
- Choosing friends
- Choosing a romantic partner
- Family life and household decisions
- Personal hobbies
- Religious or philosophical beliefs
|
The law routinely regulates interactions in the public sphere because interactions are systematic, e.g. when you interact with a shopkeeper, your primary purpose is commercial rather than personal. Your personality and individuality come second when interacting in the public sphere, as the sole purpose of your interaction is to fulfil a role within society. When you interact with the private sphere, that is when your personality is put at the forefront, and you're allowed to express your own subjective preferences, however imperfect.
Implicit in your argument is an assumption that we should move romantic relationships from the private sphere to the public sphere, as in moving them from a personal interaction to an interaction with society and something that should be regulated. This is wrong because romantic relationships are voluntary, intimate, and private, and the consequences of discriminating in them are personal rather than political or economic. It would also lead to a floodgates argument where romantic relationships could be regulated in other categories. Perhaps you would be able to sue in the event of an unfair breakup, or a one-sided relationship, or for nasty comments made by one partner. These are not nice, but they're strictly personal matters. So when a white confederate refuses to date a black person (I'm not endorsing this, but making an argument), they are acting in their own capacity, but if they then attend a 9-5 shift as a cashier and refuse to serve the same customer, they are acting in the capacity as the representative of a business interacting with society. These are two completely different means of interacting with other humans, one personal and the other systematic, and so should be treated in very different ways by the law. And that is why "racial preferences" in dating out not be treated as illegal racial discrimination.