Race(genetic relatedness within certain bounds) isn't purely skin colour, race is a whole host genetic expressions that develop over time in response to selection factors in an environment. Skin colour being one of the more visible of these genetic expressions.

Black people don't commit more murders because they're black - they commit more murders because they live in under-resourced, under-educated, poor communities

That's a hypothesis. You're free to go about proving or evidencing your position in whatever way you see fit then presenting your data to our peers for evaluation.

The unfortunate fact is that blacks have elevated levels of criminality compared to other races across all socio-economic categories.

A white person and a black person are equally likely to commit a murder given the same set of circumstances

Again, this is a hypothesis and you are free to try and establish a base of evidence to support it(although good science simply evaluates hypotheses against impartially collected evidence). A couple things off the top of my head you may be interested in as you evaluate this hypothesis.

I believe there have been studies looking into racial variability among things like impulse control, and what is known as "future time horizon." I can't seem to find any of them at the moment.

Another thing to consider, there are a number of very poor white areas in the US, I think some of the poorest counties in the US are mostly white. I'm also pretty sure the crime rates in those areas are not as high as comparable black areas. Feel free to double check that.

Implying that blackness is a causal factor is both entirely wrong and

I don't know how you got that implication from my previous comment which simply stated the fact that the crime rate among blacks is much higher than among whites and other races.

hugely racist.

If you want to discuss these matters productively it's really best to avoid jumping to words such as "racist" that, when not clearly describing obscene behavior, are just used in attempt to discredit other people.