I feel I shouldn't apologize to my best friend about disrespecting his dead mom
It sounds like you did something bad. Why are you not apologizing?
Because I have enough of being mocked for having a bad friend.
It is difficult when people are mocking you to handle things politely but if you hurt your friend you should apologize. Otherwise you will lose the friendship forever.
He's been making me look bad since I acted like a jerk in the first place, I need to defend my reputation and my own standards.
I think it could be the straw that breaks the camel's back because his mother died, and it must have been very traumatic for him. So I still think you should apologize because it's the right thing to do. Your friend might not be able to move past this, so I think it is bigger than how you feel.