Hate Crimes have already been defined by law.

...A hate crime (click here) is a traditional offense like murder, arson, or vandalism with an added element of bias. For the purposes of collecting statistics, the FBI has defined a hate crime as a “criminal offense against a person or property motivated in whole or in part by an offender’s bias against a race, religion, disability, sexual orientation, ethnicity, gender, or gender identity.” Hate itself is not a crime—and the FBI is mindful of protecting freedom of speech and other civil liberties....

Title 18, U.S.C., Section 249 

This statute makes it unlawful to willfully cause bodily injury (click here) —or attempting to do so with fire, firearm, or other dangerous weapon—when 1) the crime was committed because of the actual or perceived race, color, religion, national origin of any person, or 2) the crime was committed because of the actual or perceived religion, national origin, gender, sexual orientation, gender identity, or disability of any person and the crime affected interstate or foreign commerce or occurred within federal special maritime and territorial jurisdiction.

The law also provides funding and technical assistance to state, local, and tribal jurisdictions to help them to more effectively investigate, prosecute, and prevent hate crimes.

The law provides for a maximum 10–year prison term, unless death (or attempts to kill) results from the offense, or unless the offense includes kidnapping or attempted kidnapping, or aggravated sexual abuse or attempted aggravated sexual abuse. For offenses not resulting in death, there is a seven–year statute of limitations. For offenses resulting in death, there is no statute of limitations....

Title 18, U.S.C., Section 242 - Deprivation of Rights Under Color of Law

Title 18, U.S.C., Section 245 - Federally Protected Activities

Title 18, U.S.C., Section 247 - Church Arson Prevention Act of 1996

Title 18, U.S.C., Section 248 - Freedom of Access to Clinic Entrances (FACE) Act

Title 18, U.S.C., Section 844(h) - Federal Explosives Control Statute

Title 42, U.S.C., Section 3631 - Criminal Interference with Right to Fair Housing

Title 42, U.S.C., Section 14141 - Pattern and Practice