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This is why Trump has to be VERY careful about the deportations, and have a dang good reason (he does) for removing habeas corpus even for illegals.

Suspension of the privilege of the writ of habeas corpus is found in Article I which lists the powers of the Legislative branch. It is a Legislative power which which may be exercised directly by the Legislature, or they may delegate it to the Executive. No such power has been delegated to President Trump, nor is it likely to be delegated.

Ex Parte Bollman and Swartwout, 8 U.S. 75 (1807), Marshall, CJ

But this point also is decided in Hamilton's Case and in Burford's Case.
If at any time the public safety should require the suspension of the powers vested by this act in the courts of the United States, it is for the legislature to say so.
That question depends on political considerations, on which the legislature is to decide. Until the legislative will be expressed, this Court can only see its duty, and must obey the laws.

The Privilege of the Writ of Habeas Corpus shall not be suspended, unless when in Cases of Rebellion or Invasion the public Safety may require it.

It’s a privilege, not a right.
Citizens have it and your argument that the legislature must suspend it for them may be correct.

Article 4, Section 2

The Citizens of each State shall be entitled to all Privileges and Immunities of Citizens in the several States.

Amendment XIV

1: All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.

Invaders don’t have the privilege in the first place, so Trump can suspend it for them.