I have had the same issue but I am using a Samsung tab S tablet and currently upto 122 people in my vault. I have some other minor issue like randomly people or picked up and moved to another room but this one is very frustrating because it will actually tell me my progress as I complete part of the objective but I am not able to open the objective menu from any menu even when the progress meter pops up. I do not want to delete and re-install as the investment is greater than starting over.
Yes, the fix is here, I tried it and it worked:
http://www.gamesas.com/topic/1532994-objectives-crash-my-game/#entry24282128