Speaking of other gospels with no bearing on the Gospel we are to follow.
No, Jesus does not specifically say go and work out all your problems before doing His will, since He doesn't seem to put working out our own problems and doing His will as two conflicting commands. Likewise, Christ did not say 'I have not come to call sinners to repentance, but rather to inspire them to fix the socio-economic problems of the Roman Empire as first priority."
If I had ever heard anyone make the argument they rebut then perhaps I could see it. But I've heard this preached on many times in all three major Christian traditions - Protestant, Catholic and Orthodox - and in my limited experience, I have never heard a single individual suggest the narrative's lesson is that we should avoid helping others until we become pure and perfect. Despite Mark's insistence to the contrary, I've just not heard it, and until this, it had never entered my mind as a possible interpretation of this text. Heck, I've never heard a person make the argument that we should focus on making ourselves pure before helping others no matter what biblical passage was in question.
I would suggest to Ms. Weiss and Mr. Shea that if they think the Gospel call is for us to not concern ourselves with the evils in our own hearts as we continue to sin and sin boldly, so much as fixing the socio-economic and political problems of the world (no doubt from a political unbiased perspective), it might be time to go back to RCIA. For the rest of us, when you see people twisting the teachings of the Faith the way Perchik did to fit his Marxist ideology in Fiddler on the Roof, it's a good bet you should avoid listening to them where issues like salvation and our eternal destinies are concerned. Just saying.
Oh, and just for the record, I'm being charitable here. I'm hoping they're not rebutting the Christian teaching that our ultimate problems in the world are our separation from God and the sin of our hearts. I'm giving them the benefit of the doubt and assuming they aren't embracing the very secular and anti-religious idea that society's problems are all about failure to adhere to infallible policies and political solutions as put forth by particular political activism and ideology. I'm leaving my take as it being merely their disastrously bad exegesis of Scripture.