We do not provide support (and naturally there is no direct cost involved). We develop and test GanttProject with OpenJDK only. It may (likely) or may not (because of many reasons which we cannot predict) work with Java Runtimes from other vendors.
For the record, to minimize terminological misunderstanding: there are no “Java alternatives”. There are different vendors of Java Runtime, but all their runtimes are Java. Oracle is also a vendor of is own Java Runtime.