I was actually surprised about that in the other direction. Police consistently poll in the top 3 most trusted organizations in the country. I would have thought ICE would get the benefit of that sentiment. But in the Harvard-Harris polling above, police are +39 net favorability, while ICE is -6.
The lower polling on ICE is odd because, as a policy issue, deporting all illegal immigrants (not just ones who have committed crimes) is polling at 55-45. What other way do people think there is to deport 20+ million people?