Given that anyone who would try to vote by showing a photo ID issued by their gym or warehouse club probably should be disenfranchised due to sheer stupidity, the wording could easily be amended to incorporate the ACLU’s suggestion. Certainly, the term “government-issued photo ID” could be employed without seriously impacting the results.
Even that may not be good enough. A student ID from a state university would be a "government issued photo ID". However, it would omit one important item: the student's place of residence. The student could then vote at the campus polling place using student ID, his off-campus residence poll using his passport, and back at his parent's home using his driver's license.