Revised for clarity in light of comments
State and local police can arrest anyone who they have probable cause to believe is breaking state or local law.
Like all LEOs, Federal LEOs can break some state and local laws while enforcing Federal law. When they grab someone off the street and hold them in a cell, they are detaining them, not kidnapping them, and so on. However, to avoid arrest, the Feds have to identify themselves. That's because state and local LEO who know they are dealing with Feds on federal business no longer have probable cause to believe a crime is being committed.
State and local police can arrest Federal LEOs who they: a) have probable cause to believe are breaking state or local; and, b) have no reason to believe are Feds enforcing Federal law. In other words: Any Fed who refuses to identify herself to a local LEO can be arrested if there is probable cause.
State and local police cannot, however, arrest Federal LEOs just because they are not wearing insignias. That is because: a) there are no federal statutes requiring federal LEOs to identify themselves; b) the Supremacy Clause says federal law takes precedence over state and local law that conflict with it; c) at least in Portland, the feds were not operating under any sort of formal agreement with Portland or Oregon officials that required them to have identification.
While it is hard to prove a negative, the question of whether Federal LEOs are required to identify themselves has been looked at recently by reputable sources. They all agree there is no such law. For example, the answer from Lawfare:
Broadly speaking, law enforcement officers do not have a legal duty to disclose either their identities or their agencies of affiliation, even if asked directly. Certain municipalities require police officers to identify themselves if asked, but there is currently no federal statute requiring officer disclosure of such information.
The article points out that the two main types of cases involving police identifying themselves really don't apply: police who are working undercover, notably in sting operations, and police searching and seizing property.
They go on to point out:
Separate from the question of federal law, several states have adopted laws and regulations requiring law enforcement to identify themselves. For example, under New York City’s Right to Know Act, a broad set of police reforms that went into effect in October 2018, officers must tell civilians at the start of some interactions “their name, rank, command, and shield number.”
(Also, many departments have policies that generally require officers to identify themselves, although with exceptions. You can see examples of the policies here.)
Again, these local laws do not apply to Feds because of the Supremacy Clause.
NOTE: As several of the news stories note, the lack of identification will make it very hard to hold Federal LEOs accountable for their actions. Accountability requires identity.