Surprisingly, in India if people would be against such a measure then only because it would violate the modesty of women, and not because it invades the privacy.
https://thewire.in/24713/aadhaar-identification-simplified-m...
The UIDAI has emphasised several times that information related to religion or caste is neither collected nor stored in the Aadhaar database. Applicants and holders are encouraged to look at their Aadhaar to confirm this
All the points you say sound like you're 'prepared' or 'rehearsed' to say things like this.
When the next Gujarat riots happen, trust me just a list of people and their addresses would be sufficient enough to figure out where all the Muslims live.