This is exactly the sort of mentality that kills the passion that fuels activism as the message is…

I think the point that you’re trying to make is disingenuous. Asking someone to examine their motives does not automatically exclude anyone. The idea is not at all, “before I accept your support, you must admit that you are inadequate”, but rather, “welcome to the party, can you help me to trust you through further conversation and understanding”. 
We can and will work together, but adopting a defensive attitude in the face of a mistrust that is entirely legitimate and has been reinforced by white activism time and time again will get us nowhere.

Put in the work. Show tf up. Try to stop internalizing these negative feelings and open yourself up to conversation and self-examination.