ICE agents are refusing to carry their badges. That is one of the main issues here. They even more so refuse to display or even present their badges. They are now even not being issued badges in some cases.
If they were presenting their badges, they would not be unidentified. They would be identified, so not covered by this thread.
We can look on the ICE raid on 7500 South Shore Drive in Chicago, "They threw flashbang grenades into the corridors, smashed in doors and then marched everyone, including children, into the street in their pyjamas." About half the residents were not just natural born American citizens, but Black so their ancestors had been here since before 1808. They had hand grenades thrown into their home, and their doors smashed for having neighbors who were asylum seekers.
There is a gray area about exactly how far you can go. Displaying just "police" without a specific department is usually OK, as long as you do not try to identify yourself further as a police officer. When ICE identify themselves as being in a particular local police department, that is absolutely illegal.
But Noem says they have absolute immunity, and if that is true they can break any law they want.