It’s actually Constitutional interpretation rather than due process; again, Trump isn’t be charged with a crime, his life, liberty or property are not in jeopardy – this would be in the category of Bush v. Gore and Nixon v. US.
The Court will likely side-step the issue concerning what does or doesn’t constitute insurrection and focus instead on whether the presidency falls under the disqualification provision.
“There is an argument that because the President is not covered explicitly by the provision, the presidency itself is exempt from the disqualification.” ibid
And given the ideological makeup of the Court, it will no doubt rule that the presidency is not subject to Section 3 disqualification, placing Trump on each states’ ballot.