Several posters have given their opinion that a crime (e.g., assault) stands on its own and the motivation (e.g., hatred) is irrelevant to the legal proceedings.
Based on my reading of current US Federal Law (as I discussed above), the laws in the United States about "hate crime" vs. "regular crime" can be summarized as follows:
1. If you hate a person for an individual reason (e.g., he's a jerk, he's your boss, he stole your girlfriend), you cannot control your emotions, and you assault him, that is a "regular crime".
2. If you hate a recognizable group (e.g. race, religion, sexual orientation) and commit assault against a random member of that group or a larger number (e.g., congregation), the law may presume that this act was not only an assault on the specific victims, but an attempt to intimidate the larger group. In that case, the statutes against "hate crime" may come into effect.
I don't know what Magna Carta says about that issue in other countries.