Is that true? If the murder is racially motivated and thus a hate crime, isn't the sentence longer?

That's a comparatively recent law though. Hasn't been always the case (e.g. colonialists used to have "open hunting season" for native populations at certain times and it wasn't at all like killing one of their own race). And I doubt in the 30s South killing a black person was "equally illegal" as killing a white person (if not in law, surely in practical legal outcomes -- people just getting a slap on the wrist).

As for those other things (whether it's equally legally bad to kill someone regardless of "class, political belief or religious belief") all of those have been contested in actual law across societies (including western ones), even 20 and 30 years ago (and tides can always turn one way or another again).

Tell that to the soldiers spreading democracy.