Earlier quoted context omitted.
They can not. Neither US Citizens or Green Card Holders can be denied entry. Sources: https://www.aclu.org/know-your-rights/what-do-when-encounter... https://www.aclunc.org/our-work/know-your-rights/know-your-r...
They are not legally entitled to deny you entry. That doesn't mean they can't deny you entry. It means you might win a court case some day. ICE cannot legally arrest people who are citizens for no reason, and yet they have done exactly that 30% of the time by their own admission. "Knowing your rights" is meaningless if the public chooses to vote for people who don't care about those rights, and celebrate when you do…
I can no longer modify, retract, edit, etc my comment. This statement is almost certainly false, and I made it without due diligence to confirm I remembered the wording of a claim ICE made.
We know ICE has arrested some people who are American citizens, but we do not have anything near enough good data to make anything close to the claim I made.
This is a record of my error. Remember this if you see my comments again.