Let's put aside whether or not surveillance is necessary.
The very big problem I have here is that ICE is not the agency that should be doing this sort of surveillance. Their role is immigration control, not leftist or citizen control. If they suspect there's some dangerous criminal problem going on, then that's the role of the FBI to investigate.
The specific reason they are doing this is because ICE doesn't use traditional courts for most of their actions. As such, they are fairly unaccountable.
ICE also isn't even technically criminal law enforcement, they are civil law enforcers. They are supposed to involve local law enforcement or federal law enforcement when going after criminals. Their roles are, instead, to dish out tickets. The fact that they've been militarized is a major problem. CBP is the only agency under the DHS that is supposed to have any sort of military equipment and general detention powers and those are only supposed to be exerted at a border.
HSI has long been criminal enforcement within ICE, but I agree that they are the wrong agency to investigate this. They're doing it because they're unquestioningly loyal to Trump and because it's likely the administration has ordered certain outcomes.
I would also argue that there are no potential benefits that would make this sort of surveillance acceptable, let alone necessary.
Constitutional rights extend everywhere the Constitution covers regardless of immigration status. If ICE is conducting business in opposition to rights conveyed by the Constitution then you have found a far more grave concern to address.