So-called "sanctuary cities" have made the judgement that their law enforcement apparatus will be more effective if people who fear immigration authorities are willing to interface with it. They can't and don't stop enforcement actions by federal authorities (see Chicago, right now) - but they view active cooperation with those efforts as detrimental to other law enforcement activities. You might disagree with that assessment, but it is a straightforward exercise of the municipal power to allocate its own resources.

Claiming that they are "there to shelter people who enter the country illegally" is disingenuous at best. In reality, that is neither the goal nor the effect.