Yes, that's true, murder effects everyone in different ways. You're right in your earlier post that if both crimes are the same act, then they should recieve equal justice. Where I and others would disagree with you is that why you kill someone does matter in the amount of damage it does to a community. Take for example a woman that murdered her husband for life insurance money. Does she deserve jail time? Well ofcourse. Does anyone else in the community really need to fear her? I would say no. It was one person, for a very specific reason, and a very specific situation.
The other man, that murdered someone for being gay however, I would say causes more damage. Since its done out of hate, an entire minority feels fear and pressure. It's much more psychologically damaging. If all murders produced the exact same amount of damage, (which seems to be your opinion correct me if I'm mistaken) you would see bills going through the senate titled the "Don't kill your husband for life insurance act." Sure, incidents like those are painful, but they obviously don't cause as much of an uproar in the community as when you take someones life for who they are.
So I agree with you. All murder hurts everyone. Where I agree to disagree with you, and I believe the facts support me on this, is that hate crimes in particular cause more damage even if the raw actions are the same.