The 14th Amendment does not say "privileges NOT rights" (emphasis added) - as you stated. It says privileges and immunities of citizens of the United States. It also reiterates the right to life, liberty and property of the people. So whatever the scope of the privileges and immunities, they are in addition to the rights of the people, they do not replace them.
Thus the federal government is still bound by the 5th amendment whether you consider yourself a person of the united states or a citizen of the united states or both.
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