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They cannot (lawfully) deny entry. But they can admit you and then immediately detain and/or arrest you.

• rootusrootus 1mo ago
  Sure, if they have a warrant or probable cause, just like any other law enforcement officer.
  • kelnos 1mo ago
    In theory, yes, but in practice they can do whatever they want, and suing them after the fact is going to be expensive, and have a high probability of not working out for you. When interacting with border officials (or any LEOs, for that matter), be polite, don't get hostile or aggressive, but also be firm and don't volunteer any information that you're not required to give.
  • inigyou 1mo ago
    Not unlocking your phone is probable cause. Non-criminals readily submit for inspection. (We can fix this by refusing inspection even when we are not criminals)