Here's an interesting piece noting how Obama Homeland Security secretary Jeh Johnson defended the embattled Immigration and Customs Enforcement division.
"During the Vietnam War, millions of Americans demanded an end to the war; no one seriously demanded that we abolish the entire Defense Department," Johnson wrote in an op-ed for the Washington Post. "Obviously, that would have completely compromised national security."
Quite a few folks on the left have urged ICE's demise. However, no customs and open borders is likely not the end result most ICE-bashers would want. They might like open borders for people but are often not exactly free traders. No ICE would mean no customs checks, thus open season for importing stuff from overseas.
What they want is a less harsh immigration policy, with the recent uproar over undocumented kids getting separated from their parents creating the ICE-breaking mood on the left. Their cries were answered on that issue, as many conservatives, especially religious conservatives. joined them in criticizing the policy on pro-family grounds. The Trump team took note, did a 180 and are working at reunification fairly promptly with a bit of administrative foot-dragging.
However, if you abolish ICE, you'll likely have some agency doing the custom checks and immigration checks. The resulting agency will resemble ICE and likely have a large hunk of the same staff, as creating a new agency while black-balling former ICE-people will be reinventing the wheel to a dangerous degree.
I have the same response to conservatives who want to abolish the IRS. We need to have someone collecting taxes, and those folks will typically not be well like. Jesus got ragged on for hanging out with "tax collectors and sinners"; their reputation is somewhat better today, but few people like paying taxes.
The IRS has to play bad cop from time to time, auditing folks at random and calling BS when folks fail to pay up. Likewise, ICE has to play bad cop, stopping contraband and under-documented folks at the border and doing the occasional snatch of folks who overstayed their welcome or who weren't invited into the country in the first place. Those folks aren't well liked, either, especially if you're of an ethnic group getting the white-glove treatment from ICE.
However, as Mike Rowe would say. somebody's gotta do it. How much enforcement to do is a live issue. The fact that some level of enforcement is needed should be a no-brainer.