Are we allowed to edit textures in runs? for example if i changed the raygun texture to gold would that be allowed. or changing the EE songs to something else?

Editing Textures in runs is not allowed since it can cause crashes and unfairness for other players. Changing the EE song is not allowed. However, you can use these textures for offline play if you wish just not on speed runs.

How so would it cause unfairness. If it's just changing the backround textures to make it more entertaining or whatever they feel then how so is this unfair. This is done in hundreds of runs on black ops 1 and 2 games. What's bad of having it on this game. If it does somehow cause crashing in a run then so be it. But if a run is done successfully with just a bit of funny textures in the backround. I dont really see a problem with that.

Yeah you're right, after doing some research, it doesn't cause unfairness.

so whats the definitive answer

Yes, your allowed to edit textures in COD: BOZ during speedruns.