No, that is not what conservatives say. Conservatives say a lot of things but that is not one of them. What I say is you cannot legislate intention or thought. If I, as a white guy, beat up a black guy and I call him an idiot, does that mean I like that guy more than if I called him a racial slur? I would think that if I beat up a black guy I must already have some type of hatred towards that guy. So does it really matter if I hate the guy or hate his race, it is still the guy I am beating up and not the race.
Of course I would never beat up a black guy, but the point is, what is the difference does it make of what kind of hate I would have for this guy? Hate is hate.
Now there is are other situations. What if the black guy punched me in the face, said something disparaging about my race and then I punch him back and said something about his race. The police see it happen, who gets charged with the hate crime. The black guy who started the fight or me? Or do both of us? What if I only said that because he upset me so much by punching me in the face?
I think legislating thought exceeds the governments authority. If they can do it for racial reasons then they can make excuses for all sorts of reasons and we are now seeing the beginning of all of that with cancel culture. Any government would just love to have the power to destroy lives because they didn't think the right way. Many governments have taken that power. One government in particular used it against Jews.