Whether a person meets Constitutional requirements is a question of law, not politics. The Judiciary handles questions of law, they find facts and apply law.
“No Person except a natural born Citizen [] shall be eligible to the Office of President” is a requirement no different than the requirement that the eligible person shall “have attained to the Age of thirty five Years” and the requirement that they have “been fourteen Years a Resident within the United States” - they all are judicable.
To contend that eligibility is determined politically renders the Constitutional requirements a nullity.
Courts do not provide answers to all questions or issues.
Just as it is not the job of the judiciary to appoint ambassadors, to grant pardons, to impeach presidents, to declare war or to impose taxes, it is not the job of the judiciary to choose Presidents. I believe that the Constitution very clearly delegates to Electors the responsibility for choosing our presidents.
I believe that is why you have never seen a court attempt to disqualify any candidate for President. And, if you are a voter, you participate in the election of Electors. You must take that responsibility seriously and you should not vote for an Elector who is pledged to support an unqualified candidate.
If Ted Cruz was not qualified to be President, I would not vote for Electors who pledge themselves to support his candidacy. However, Ted Cruz was a citizen at birth. He is, therefore, a natural born citizen and he is, therefore, qualified to be President. If he is on my ballot, I will vote for him.