Voting is a privilege. Checks are necessary to prevent felons and criminals from voting.
Guns, however, are constitutional rights. “Background check” is a violation of the fundamental rights.
The fourth section of Article Four requires the United States to guarantee to each state a republican form of government... to do this citizens must be allowed to vote. As such the Supreme Court has already established that the right to vote is an unenumerated right as per the 9th Amendment.
Voting is a right. One that has been amended in the constitution to define for whom the right applies... twice.
But your correct that if a check is required for the 2nd it should just as well - if not more importantly - be applied for the vote.