Economic justice does not always translate directly into social justice. (Witness the many times in history in which relative economic equality did not assure social justice: the Jews of Nazi-era Germany, for instance, who were well integrated into German society at that time. It didn't prevent Jewish professors and scientists from being removed from their positions, or even wealthy Jews from having their property confiscated and being sent to death camps. I take this only as a well-known and extreme example; but other examples abound throughout the world in recent decades and even today.)
Your argument makes sense until one realizes that it started out, somewhat tautologically, with the tacit assumption that "poverty" alone is the basis of social injustice. That's not quite right. It doesn't explain why women face barriers in their careers far beyond what males experience. Or why middle-class and even very upper-class African-Americans are pulled over by the police in alarmingly higher numbers than whites. Or why someone who applies for jobs with a Hispanic or black-identified surname gets fewer replies or call-backs than the same resume with a waspy name attached. It doesn't explain bias against gay or transgender people who in many cases are not economically disadvantaged at all.
Both issues are important, but they are not the same. Racial, religious, or ethnic intolerance is not always magically eradicated by economic standing. There are deeper seated issues of "otherness" and bias that also play significantly into social justice. Failure to recognize this will be a failure to address fundamental issues of intolerance and justice.