People have mixed feelings about the police because the police have two mixed roles; peace keeper and regulation enforcer.
The peace keeper is respected and admired. Peace keepers are heroes and friends. Children want to grow up to be peace keepers. People like to help the peace keepers do their job.
Peace keepers don't have to be busy, their visible presence discourages violence, that's why they wear uniforms. Since they can be friends to all but the violent they form strong bonds with the people in their communities. People call on peace keepers when they need them by dialing 911 or shouting "help! police!". People generally join the police because they want to be peace keepers.
Regulation enforcers are generally despised and avoided. Few are proud have regulation enforcers for friends. Children rarely want to grow up to be regulation enforcers. Regulation enforcers have to stay busy to do their job and to reduce their visibility they often avoid wearing uniforms. Since there are far more regulations than people are willing to obey there is always more work to do. Instead of waiting for some problem to occur they use expensive equipment and careful planning to seek out violators. When violators hide they request bigger budgets to ferret them out. To keep their identities secret regulation enforcers rarely form strong bonds in their communities. Few people join the police in order to become regulation enforcers.
In recent times there has been a change in the role of the police from peace keeper to regulation enforcer. This change is due to excessive regulation. The libertarians favor massive deregulation so the police can go back to being the peace keepers we respect and admire instead of the regulation enforcers we despise and avoid.