Hirschhorn was within Kurmainz (the prince-archbishopric and electorate of Mainz) until 1803, when it was allocated to Hesse-Darmstadt (which became a grand duchy in 1806). Kurmainz, being ruled by the Catholic archbishop of Mainz, was arch-Catholic; as late as 1824 (per German wikipedia), there were only 25 Protestants out of 1507 total population in Hirschhorn. So chances are that Karl was at least born Catholic, though he perhaps converted when he entered the (Protestant) grand duke's administration.
The Catholic parish records for this area are not online (if they were, they would be at matricula-online.eu), and it appears there are no Protestant records for this area at archion.de, either.