This is not a criminal trial. Yet anyway.
It's a matter of asking a job applicant to demonstrate he has qualifications for the job. Like providing a college or high transcript when the job requires a degree. Like providing a birth certificate when the job requires citizenship. (Or alternatively naturalization paperwork). We've all had to do one or more of those things, why should a Presidential candidate not do the same.
Yes no other such Candidate has needed to that, but then none of them had foreign citizens fathers and stepfathers either.
It's not as if providing the certificate need be a big invasion of privacy. The Certificate could be provided to an appropriate court, preferably the Supreme Court, who could then verify that he does, or does not meet the "Natural Born Citizen" requirement. No need to release any other information on the BC.
Its never going to be a trial. The Supreme Court will deny each and every one of these case.
Further, the hearsay rule applies to civil as well as criminal trials.