Why do open access consortia affiliate themselves with questionable publishers
Why do these consortia affiliate themselves with questionable
  publishers?


Hindawi is a founding member of the OASPA and MDPI, whichever opinion we might have about the quality of its journals, is a major player in the OA business. The OASPA apparently conducted an internal investigation about MDPI and seem to be happy about the results. The question might be more: is the OASPA questionable?


  how can the academic community pressure open access consortia to
  consider their members carefully?


I would recommend not to consider open access consortia as relevant. Then, not submitting papers, not serving on the editorial board, and refusing reviewing tasks for sketchy journals.

On a more general level, one thing we could do is reduce the demand for low-quality, pay-for-publish 'OA' journals by challenging the hiring policies based on publication volume in our local institutions.