These [1] are the results of that election. Austin has a population of 950,000 residents with a voting age population of about 741,000 [2]. In total about 5% of the resident population voted to maintain the fingerprinting law and 4% to soften it. A 1% margin on a voter turnout of less than 12%.
I fully appreciate that that is a 'democratic republic in action.' I'm certain you can understand one might find it distasteful, just as one can easily understand your distaste for state level 'democratic republic in action.' I'm certain our systems made all the sense in the world hundreds of years ago. But these sort of things do not feel right today when we live in a country with counties that now have greater population than the entire country did when these laws and systems were developed.
[1] - http://traviselectionresults.com/enr/contest/display.do?crit...
[2] - https://www.census.gov/quickfacts/fact/table/austincitytexas...