>Was it life, liberty, or property the Colorado Supreme Court deprived Trump of?
You need to understand the difference between procedural due process, and substantive due process, you are citing substantive due process. In any matter, the Colorado Supreme Court is depriving its citizens of the "liberty" to elect their own representatives, and thus Trump could raise a third party claim in addition to his own "liberty" interest in being able to be in the republican primary, under the first amendment right to free association. A primary election literally does not involve presidential electors, and is supposed to be within the purview the parties themselves (which are literally corporations), which is why the democrats can have "super delegates" without violating the equal protection clause.
With regards to procedural due process, there are no "insurrection" statutes or regulations in Colorado, there is only a federal criminal statute and states do not have the ability to enforce federal criminal law, nor has there been any decision by a court of competent jurisdiction (a federal court) of insurrection, thus the state is either A) engaging in ex post facto law making in violation of the constitution, or B) exceeding the bounds of its jurisdiction (making judgements about federal criminal law).