My brother is a former police officer in Los Angeles. He said that requiring the police to inquire about a resident's immigration status just makes his job harder. It takes time away from focusing on public safety and scares many undocumented people who may have information about a crime.
You want the public to communicate and interact with the police. Immigration is a federal responsibility.
So, what do opponents say about this? Because I think a lot of opponents may not understand the reality of living in a large city (especially a port like San Fran). Police have got more than enough things to worry about without poking at that hive.