The crime is what caused the harm, not the thoughts that were spoken or the motivation behind the crime. However, what a person says before a crime can be used to demonstrate intent, premeditation, and/or motive, which all go toward defining the actual crime. Such as the difference between First Degree Murder and Manslaughter. It makes no difference, or at least it shouldn't, why the person killed another person, other than to define the actual crime. Killing a person by definition is a crime of hate. You don't murder people you like.
That a person of one race killed a person of another race should not make a difference. That a person of one religion killed a person of another religion should not make a difference. That a heterosexual killed a homosexual shouldn't make difference. That a CIS gender person killed a trans person shouldn't make a difference.
The crime is the killing. The defining of the potential charge and potential sentence can be defined in part by motive, but motive is not the crime.
One thing I use to help me evaluate if something should be utilized by me in my thinking, is to reverse or exchange terms in a statement. For instance, in a statement that includes race, I would exchange one race of another and see if the statement still stands. In this instance, we could take your statement, "I see nothing wrong with punishing such a person more severely than someone who simply acts out and shoots a Muslim, Black, Christian, Gay, Woman or whatever." and change it around to say, "I see nothing wrong with punishing such a person less severely than I would someone who shoots a Muslim, Black, Christian, Gay, Woman or whatever."
If it doesn't seem reasonable to punish a person less harshly for killing a person just because they wanted to kill a person, any person, then it's not reasonable to punish a person more severely that killed a person because of some special classification. In both cases, there would be premeditation of murder. One that chose their victim for whatever reason (ease of access, simple opportunity of circumstances, or whatever) while the other was motivated by some other factor. The crime is the same.