The process of proposing a law begins with people acting in a way contrary to what the proposed law is designed to prevent. There would be no laws against murder if no murder had ever taken place. And there would be no laws, proposed or in effect, against discrimination if there was no discrimination taking place.
As discrimination becomes less and less palatable to society, society tries to figure out a way to end the discrimination. Since you can't just tell someone to stop it and really expect them to do so, we have to resort to creating laws and attaching consequences. So when people oppose laws such as this, the logical conclusion is they don't want to have to stop discriminating against certain people. They will throw all kinds of reasons why laws like this shouldn't be passed but the real reason is they don't want to lose their right to discriminate.
The only people who would oppose laws against murder are murders, or those who are inclined to murder. It's the same with discrimination.